# Difference between revisions of "751.40 LFD Widening and Repair"

## 751.40.1 General

### 751.40.1.1 Widening and Repair of Existing Structures

The Federal Highway Administration and the States have established a goal that the LRFD standards be used on all new bridge designs after October 2007. For modification to existing structures and with the approval of the Structural Project Manager or Structural Liaison Engineer, the LRFD Specifications or the specifications which were used for the original design, may be used by the designer.

### 751.40.1.2 Steel HP Pile Maintenance and Repair

Maintenance/Repair Guidelines

Piles are primary structural members and are compressively loaded all the time which makes it important to safely inspect, maintain and repair them if necessary. Pile inspection will require an assessment of pile performance by looking for pile deterioration and measuring pile section loss in order to determine the level of pile maintenance/repair required. The following schedule may be used for selecting the level of maintenance/repair required:

Pile Percent Section Loss Method* Level
0% through 25% Clean and recoat existing piles Maintenance
>25% through 40% Encasement of deteriorated section Maintenance
>40% through 75% or holes in any element or local buckling of any element Plating ** of deteriorated section OR replacement *** of section (splicing), AND encasement of the repaired section Repair
>75% Contact the Bridge Division Repair
* Method may also include cleaning and recoating all exposed piles, and cleaning and recoating all remaining exposed pile sections after encasement and/or repair.
** Plating can be for both flanges only, web only or both flanges and web. Overall symmetry of the pile cross-section shall be maintained when plating.
*** Based on additional factors other than just the percent of pile section loss, a replacement pile section (splicing) may be considered. Minimizing or eliminating traffic loading, adding falsework or just having support conditions such as integral bents (where both the pile cap beam and the superstructure concrete diaphragm are connected by more than just dowel bars – see bridge plans) can help to determine the method of repair. A replacement pile section can be coated or galvanized. See Structural Project Manager.

Estimating Pile Percent Section Loss in the Field

Quantifying pile section loss can be inexact. To encourage uniform application of the maintenance/repair guidelines, the following procedure is recommended:

1. Pile section loss should be determined using a thickness meter.
2. Remove deteriorated material and clean pile for measurement.
3. At any point along a pile (cross-section) where there are three elements to be considered independently, e.g. two flanges and a web.
4. Estimate the actual cross-section area of each element at its most deteriorated point along the length of pile. Using the thickness meter, measure the thickness at several points along a horizontal line across the element. From this data, estimate the actual cross-section area of each element.
5. The fraction of section remaining (PSR) is the actual cross-section area of each element at its most deteriorated point along the length of pile divided by the original area of same element.
6. Percent section loss is 100(1 – PSR) for each element.
7. The greatest PSR dictates the maintenance/repair method.
8. Examine continuity at flange/web intersections. Section loss along these intersections along the length of pile of more than 6 linear inches should be repaired using encasement as either the only method or part of plating/replacing repair method regardless of a low percent section loss.
9. Interference from cross bracing at pile sections to be repaired will need special consideration not detailed on the standard drawings.

Additional types of maintenance and repairs may be considered which include but are not limited to:

• Zinc tape coating
• FRP strengthening
• Corrosion inhibitor

## 751.40.2 Typical Sections of Concrete Repairs

### 751.40.2.1 Resurfacing

PLAN

Place the following notes on plans.

The existing Asphaltic Concrete surface shall be removed to a uniform grade line (*) below the existing control grade line as noted.
Resurface with (*) Asphaltic Concrete.
(*) Depth of Asphaltic Concrete as specified in the Bridge Memorandum.

### 751.40.2.2 Special Repair Zones

The following order of repair zones shall be used for the deck repair on continuous concrete structures.

Hydro Demolition Projects (Case 1 and 2)

Conventional deck repair required in the areas designated as special repair zones shall be completed before demolition in alphabetical sequence beginning with Zone A. Zones with the same letter designation may be repaired at the same time.

Any deck repair in areas not designated as a special repair zone shall be completed after hydro demolition. Case 1 is primarily monolithic deck repair after hydro demolition. Case 2 is primarily conventional deck repair after hydro demolition.

Note:

- Case 1 shall not be used for polyester polymer and low slump concrete wearing surfaces (too stiff for monolithic repairs).
- Conventional deck repair is required with void tube replacement after hydro demolition with both Case 1 and Case 2.
- If an excessive number of zones are required at any bent, see the Structural Project Manager or Structural Liaison Engineer.
- Consider combining zones if the length of a zone in the longitudinal direction of the bridge is less than 24 inches.
(1) Development Length.
See EPG 751.50 Standard Detailing Notes for appropriate notes.

Non-Hydro Demolition Projects

Any deck repair in areas not designated as a special repair zone shall be completed prior to work in Zone A. Zones with the same letter designation may be repaired at the same time.

Note:

- If an excessive number of zones are required at any bent, see the Structural Project Manager or Structural Liaison Engineer.
- Consider combining zones if the length of a zone in the longitudinal direction of the bridge is less than 24 inches.
(1) Development Length.
See EPG 751.50 Standard Detailing Notes for appropriate notes.

### 751.40.2.3 Substructure Repair

#### 751.40.2.3.1 Formed and Unformed Repair Areas

Fig. 751.40.2.3.1.1, Elevation of Int. Bent

Fig. 751.40.2.3.1.2, Section through End Bent

#### 751.40.2.3.2 Bent Cap Shear Strengthening using FRP Wrap

Fiber Reinforced Polymer (FRP) wrap may be used for Bent Cap Shear Strengthening.

When to strengthen: When increased shear loading on an existing bent cap is required and a structural analysis shows insufficient bent cap shear resistance, bent cap shear strengthening is an option. An example of when strengthening a bent cap may be required: removing existing girder hinges and making girders continuous will draw significantly more force to the adjacent bent. An example of when strengthening a bent cap is not required: redecking a bridge where analysis shows that the existing bent cap cannot meet capacity for an HS20 truck loading, and the new deck is similar to the old deck and the existing beam is in good shape.

How to strengthen: Using FRP systems for shear strengthening follows from the guidelines set forth in NCHRP Report 678, Design of FRP System for Strengthening Concrete Girders in Shear. The method of strengthening, using either discrete strips or continuous sheets, is made optional for the contractor in accordance with NCHRP Report 678. A Bridge Standard Drawing and Bridge Special Provision have been prepared for including this work on jobs. They can be revised to specify a preferred method of strengthening if desired, strips or continuous sheet.

What condition of existing bent cap required for strengthening: If a cap is in poor shape where replacement should be considered, FRP should not be used. Otherwise, the cap beam can be repaired before applying FRP. Perform a minimum load check using (1.1DL + 0.75(LL+I))* on the existing cap beam to prevent catastrophic failure of the beam if the FRP fails (ACI 440.2R, Guide for the Design and Construction of Externally Bonded FRP, Sections 9.2 and 9.3.3). If the factored shear resistance of the cap beam is insufficient for meeting the factored minimum load check, then FRP strengthening should not be used.

* ACI 440.2R – Guide for the Design and Construction of Externally Bonded FRP

Design force (net shear strength loading): Strengthening a bent cap requires determining the net factored shear loading that the cap beam must carry in excess of its unstrengthened factored shear capacity, or resistance. The FRP system is then designed by the manufacturer to meet this net factored shear load, or design force. The design force for a bent cap strengthening is calculated considering AASHTO LFD where the factored load is the standard Load Factor Group I load case. To determine design force that the FRP must carry alone, the factored strength of the bent cap, which is 0.85 x nominal strength according to LFD design, is subtracted out to give the net factored shear load that the FRP must resist by itself. NCHRP Report 678 is referenced in the special provisions as guidelines for the contractor and the manufacturer to follow. The report and its examples use AAHTO LRFD. Regardless, the load factor case is given and it is left to the manufacturer to provide for a satisfactory factor of safety based on their FRP system.

Other References:

### 751.40.2.5 Temporary Traffic Control Device

Show Barrier as per district recommendation. Typically Barrier is shown when structure is on interstate and/or the rail is being removed. Otherwise, show the dimension lines with 2'-0" dimension.

(* If this dimension is less than 3 feet, the temporary concrete traffic barrier shall be attached with tie-down straps, with the approval of the Structural Project Manager or Structural Liaison Engineer. Where lateral deflection cannot be tolerated, the temporary concrete traffic barrier shall be attached with the bolt through deck detail (to be used only on existing decks). See EPG 617.1 Temporary Traffic Barriers and EPG 751.1.2.12 Temporary Barriers.
(** Where slab removal represents small and discontinuous openings in the deck along the bridge length (i.e. expansion device replacement) use of either a flat steel plate, a 22 ½” temporary traffic control device or a temporary concrete traffic barrier may be more appropriate. Consult with the Structural Project Manager or Structural Liaison Engineer.

## 751.40.3 Dimensions

### 751.40.3.1 Wearing Surfaces

Replacement of Typical Expansion Joint Systems (Strip Seal Shown, Other Systems Similar)

When concrete is removed and armor is replaced, see EPG 751.13 Expansion Joint Systems for the appropriate expansion joint system details and EPG 751.50 H5 for the appropriate notes.

For chip seals and polymer wearing surfaces, see EPG 751.50 I1 for the appropriate notes.

Elastomeric Expansion Joint System

When a thick wearing surface (low slump, latex, silica fume, CSA cement, steel fiber reinforced, asphaltic) is used, the elastomeric joint must be replace by another type of expansion joint system.

Flat Plate Expansion Joint System

(* When this dimension exceeds 3" and a concrete wearing surface is used, tack weld a one inch bar chair to the plate for each 3" of plate to be covered by the wearing surface.
(** Scarify existing slab. See the Bridge Memorandum for the minimum depth of scarification. Scarification not required for asphaltic concrete wearing surface.
Note: See standard plans for Steel Dams at Expansion Joints.

LATEX, LOW SLUMP, SILICA FUME, ASPHALTIC OR EPOXY POLYMER

TYPICAL SECTION OF EXISTING CURB
OUTLET SHOWING LIMITS OF EPOXY SEAL

Note:

(*) Dimension to edge of girder or stringer ±. For bridges that do not have girders or stringers use 2'-6", except that if with thrie beam rail, then use 4'-0".

Consult with Structural Project Manager or Liaison for making work incidental to another item or use of pay item "Clean and Epoxy Seal".

TYPICAL ELEVATION OF EXISTING CURB
OUTLET SHOWING LIMITS OF EPOXY SEAL

(Wearing surface not shown for clarity)

SLAB EDGE REPAIR

If slab edge repair is specified on the Bridge Memorandum when the barrier or railing is not removed or when full depth repair is not a pay item, the following detail shall be provided.

CONCRETE EDGE REPAIR

If the barrier or railing is removed when full depth repair and slab edge repair are pay items, the following detail shall be provided.

CONCRETE EDGE REPAIR

* If the dimension exceeds 4 inches, the repair extending to the edge of slab will be paid for as Full Depth Repair.

### 751.40.3.2 Longitudinal Joint Details

REPLACEMENT OF EXISTING EXPANSION DEVICE

MEDIAN BARRIER

SECTION THRU BARRIER

DETAIL "A"

 (1) May be cast vertical and saw cut to slant. (*) Latex Concrete Wearing Surface = 1-3/4".Low Slump Concrete Wearing Surface = 2-1/4". (**) Cut minimum 1/2" support notch (rough finish). Remove any existing compression seal.

## 751.40.4 Railing End Treatments

### 751.40.4.1 Replacement of Existing Curb and Parapet Barrier with New Concrete Barrier

NON-INTEGRAL END BENTS

 EXISTING BARRIER PROPOSED BARRIER SECTIONS THRU WING

 Note: Remove existing barrier above lower construction joint. For details not shown, see EPG 751.12 Protective Barricades.

 EXISTING BARRIER PROPOSED BARRIER SECTIONS THRU SLAB

INTEGRAL END BENTS

 EXISTING BARRIER PROPOSED BARRIER SECTIONS THRU WING

 Note: Remove existing barrier above lower construction joint.

 EXISTING BARRIER PROPOSED BARRIER SECTIONS THRU SLAB

### 751.40.4.2 Replacement of Existing Barrier or Railing Using Anchor Systems

NEW BARRIER ON SLAB

SECTION THRU BARRIER

SECTION THRU BARRIER
(OPTIONAL ANCHORING SYSTEM)

Note: See EPG 751.50 I2. Resin & Cone Anchors for appropriate notes.

NEW BARRIER ON WING

SECTION THRU BARRIER(*)

SECTION THRU BARRIER(*)
(OPTIONAL ANCHORING SYSTEM)

Note: See EPG 751.50 I2. Resin & Cone Anchors for appropriate notes. For details not shown, see EPG 751.12 Protective Barricades.

REPLACEMENT OF EXISTING BARRIER AT END OF WING USING ANCHOR SYSTEMS

INTEGRAL END BENTS

 (*) Extend existing horizontal bars2'-3" into new concrete. (**) Fit bar to follow transition face of barrier. Note: For details of guardrail attachment, see barrier standard drawings.
ANCHOR SYSTEMS AT SECTION C-C PART ELEVATION

 SECTION A-A SECTION B-B SECTION C-C

REPLACEMENT OF EXISTING BARRIER AT END OF WING USING ANCHOR SYSTEMS

NON-INTEGRAL END BENTS

 (*) Extend existing horizontal bars2'-3" into new concrete. (**) Fit bar to follow transition face of barrier. Note: For details of guardrail attachment, see barrier standard drawings.
ANCHOR SYSTEMS AT SECTION C-C PART ELEVATION

 SECTION A-A SECTION B-B SECTION C-C

### 751.40.4.3 Replacement of Existing Rail with Thrie Beam Rail

As a matter of policy, blockouts for thrie beam railings are required while FHWA does show similar systems without blockouts as NCHRP 350 approved. See the Structural Project Manager (SPM) or the Structural Liaison Engineer (SLE), if practical, to omit blockout. A design exception shall be required. Blockouts shall always be required on NHS routes.

There are four systems for use on state routes. In these four systems the connection design load used is 1.5 times plastic moment capacity (Mp) of W6 x 20 Post. The vertical clearance of System 3 shall be checked due to the obtruding lower connection.

### 751.40.4.4 End Treatment Using Thrie Beam Rail

Guidance for Design:

Adequate clearance to first post off bridge shall be required. (See also Standard Plan 617.10 for new bridges.)

## 751.40.5 Drainage

### 751.40.5.1 Structure with Wearing Surface Slab Drains - Details

Two material options may be used for slab drains:

1. Steel Slab Drains and inserts are only shown in the following details.
2. Fiberglass Reinforced Polymer (FRP) drains may be used with the approval of the Structural Project Manager or Structural Liaison Engineer. See EPG 751.10.3.2.1 New Structure Without Wearing Surface Slab Drains - Details for guidance and details of FRP drains on new structures as an aid.
A positive mechanical connection must be used for attaching FRP drains to either existing steel drains or to new FRP inserts since welding cannot be used as is shown in the following details for steel drains. For example, using at least four bolt-through connectors (one per side) from new FRP drains into a new wearing surface or an existing steel drain, or using an epoxy adhesive in conjunction with at least two bolt-through connectors is required. It has been shown that using a more viscous epoxy or anchoring gel is beneficial in order to avoid dripping during placement. Using epoxy adhesive or an anchoring gel by itself is not acceptable.
FRP drain may not fit exactly to the inside or to the outside of existing steel drain. The looseness of fit can be addressed by considering a combination of attachment details like mechanical connectors (to existing slab drain) plus either a viscous epoxy adhesive or a positive attachment to an exterior girder depending on the length of the slab drain extension.

For new wearing surface over new slab, note on plans:

Piece "A" shall be cast in the concrete slab. Prior to placement of wearing surface, piece "B" shall be inserted into piece "A".

FOR STRUCTURE WITH WEARING SURFACE
(GIRDER DEPTH LESS THAN 48")

PART ELEVATION OF SLAB AT DRAIN

ELEVATION OF DRAIN
 * Deck thickness minus 1/8" minus the depth of the scarification. ** Do not include the depth of the scarification.

PLAN OF DRAIN

FOR STRUCTURE WITH WEARING SURFACE
(GIRDER DEPTH 48" AND OVER)

 ELEVATION OF DRAIN PART ELEVATION OF SLAB AT DRAIN PLAN OF DRAIN
 * If dimension is less than 1", drains shall be placed parallel to roadway. Otherwise, place drains transverse to roadway. ** Do not include the depth of the scarification. *** Deck thickness minus 1/8" minus the depth of the scarification.

 DRAIN TRANSVERSE TO ROADWAY DRAIN PARALLEL TO ROADWAY PART PLANS SHOWING BRACKET ASSEMBLY

FOR STRUCTURE WITH WEARING SURFACE
(CONTINUOUS CONCRETE STRUCTURES)

PART SECTION NEAR DRAIN

ELEVATION OF DRAIN

PLAN OF DRAIN

 * Deck thickness minus 1/8" minus the depth of the scarification. ** Do not include the depth of scarification.

FOR STRUCTURE WITH WEARING SURFACE
(VARIABLE DEPTH GIRDERS)

PART ELEVATION OF SLAB AT DRAIN

Note: For variable depth girders with drains in deeper section, let the deeper section control and use throughout the structure.

TYPICAL SECTION STRAIGHT DRAIN

### 751.40.5.2 Structure with Wearing Surface Round Slab Drains - Details

FOR STRUCTURE WITH WEARING SURFACE
MISCELLANEOUS DETAILS - ROUND DRAINS

FRP round drains may be used optionally unless otherwise specified. See EPG 751.10.3 Bridge Deck Drainage – Slab Drains for guidance and details as an aid. Specify nominal pipe size as needed referencing ASTM D2996. Specify outer diameter based on nominal pipe size necessary for drainage for coring the correct size hole in deck.

Note: See EPG 751.10.3 Bridge Deck Drainage – Slab Drain for slab drain spacing.

 TYPICAL PART PLAN SECTION SHOWING BRACKET ASSEMBLY

TYPICAL PART PLAN OF DRAIN

Note: See EPG 751.50 Standard Detailing Notes for appropriate notes.

### 751.40.5.3 Structure with Wearing Surface Raising Slab Drains or Scuppers - Details

FOR STRUCTURE WITH WEARING SURFACE
RAISING SLAB DRAINS

PART SECTION OF DRAIN

PART PLAN OF EXISTING DRAIN
Note:
Outside dimensions of drain extension are 7-1/4" x 3-1/4", and drain extension shall be galvanized in accordance with ASTM A123.

FOR STRUCTURE WITH WEARING SURFACE
RAISING SCUPPERS

TYPICAL SECTION THRU SCUPPER

PLAN OF GRATE SUPPORT
AND
PLAN OF SCUPPER EXTENSION

* Plate thicknesses should match those of existing scupper and existing grate.

## 751.40.6 Closure Pour

Note:

For closure pour on solid slab or voided slab bridges, use expansive concrete.

Release the forms before the closure pour is placed.

## 751.40.7 Design and Posting Considerations

Existing structures to redecked and/or widened should be evaluated to determine if the superstructure is considered to be structurally adequate. The structural adequacy check should be determined based on load ratings using the Load Factor Method. Strengthening of the superstructure will not be required if the minimum posting values shown below meet or exceed legal load requirements. In addition, there may be cases where the existing bridge posting is acceptable based on the bridge specific site conditions such as AADT, amount of truck traffic, overweight permit route, etc.

 1) H20 (one lane with Impact) [Posting Rating] ≥ 23 tons 2) 3S2 (one lane with impact) [Posting Rating] ≥ 40 tons

Posting Rating = 86% of Load Factor Operating Rating (Refer to figures below for H20, 3S2 and MO5 criteria).

If a structure is located within a commercial zone, then the following additional posting condition must be investigated:

 3) M05 (two lane with impact) [Operating Rating] ≥ 70 Tons (posting limit)

Any other overstresses or inadequacies (slab, substructure, etc.) shall be reported to the Structural Project Manager.

Deck thickness for redecks shall be determined such that Posting will not be required or the existing posting is not lowered, and it is generally not less than original deck thickness.

Deck thickness for widenings shall be existing thickness unless thicker slab does not create overall deck stiffening irregularities.

See Structural Project Manager if AASHTO minimum deck thickness can not be used on redecks and widenings.

Future Wearing Surface (FWS) Loadings for widenings with concrete wearing surfaces - In addition to weight of wearing surface:

Add FWS of 35 psf to the design of new girders if existing girders are sufficient for the 35 psf FWS
If existing girders are not sufficient for any FWS then lower FWS to FWS = 0.
The existing ratings should be reviewed to determine what wearing surface loads were used. When necessary, the rating should be evaluated for acceptability of the proposed changes in the wearing surface loads and geometry. Preliminary ratings that are based on estimated geometry shall be revised when the updated, final geometry is known.

## 751.40.8 Design Information when using AASHTO Standard Specifications for Highway Bridges 17th Edition

Structures shall be designed to carry the dead load, live load, impact (or dynamic effect of the live load), wind load and other forces, when they are applicable.

Members shall be designed with reference to service loads and allowable stresses as provided in AASHTO (17th edition) Service Load Design Method (Allowable Stress Design) or with reference to factored load and factored strength as provided in AASHTO Strength Design Method (Load Factor Design). Load groups represent various combination of loads and forces to which a structure may be subjected. Group loading combinations for Service Load Design and Load Factor Design are given by AASHTO (17th edition) 3.22.1 and AASHTO (17th edition) Table 3.22.1A.

The live load shall consist of the applied moving load of vehicles and pedestrians. The design live load to be used in the design of bridges for the state system will be as stated on the Bridge Memorandum.

• The design truck: HS20-44 or HS20-44 Modified
• The design tandem (Military)

Criteria

1. All widened or retrofitted bridges on the National Highway System and in commercial zones may be designed for HS20-44 Modified loading. All remaining bridges will be designed for HS20-44 loading.
2. The Design Tandem loading is to be checked on national highway system or when Alternate Military loading appears on the Bridge Memorandum.
3. Carrying members of each structure shall be investigated for the appropriate loading.
• Main carrying members include:
• Steel or Concrete stringers or girders.
• Longitudinally reinforced concrete slabs supported on transverse floor beams or substructure units (includes hollow slabs).
• Transversely reinforced concrete slabs supported by main carrying members parallel to traffic and over 8'-0" center to center. Use the formulas for moment in AASHTO Article 3.24.3.1 Case A.
• Steel grid floors when the main elements of the grid extend in a direction parallel to traffic, or with main elements transverse to traffic on supports more than 8'-0" apart.
• Timber floors and orthotropic steel decks.
4. The reduction in live load for calculating substructure members is based on AASHTO 3.12.1. See Live Load Distribution in the Load Distribution Section.

The HS20-44 truck is defined below as one 8 kip axle load and two 32 kip axle loads spaced as shown.

Varies = Variable spacing 14’ to 30’ inclusive. Spacing to be used is that which produces the maximum stresses.

HS20-44 Design Truck

(*) In the design of timber floors and orthotropic steel decks (excluding transverse beams) for H-20 Loading, one axle load of 24 kips or two axle loads of 16 kip each, spaced 4 feet apart may be used, whichever produces the greater stress, instead of the 32 kip axle load shown.

(**) For slab design, the center line of wheels shall be assumed to be one foot from face of cur

The HS20-44 Modified truck is defined below as one 10 kip axle load and two 40 kip axle loads spaced as shown. This is the same as HS20-44 truck modified by a factor of 1.25.

Varies = Variable spacing 14’ to 30’ inclusive. Spacing to be used is that which produces the maximum stresses.

HS20-44 Modified Design Truck

(*) For slab design, the center line of wheels shall be assumed to be one foot from face of curb.

The Design Tandem Loading is a two axle load each of 24 kips. These axles are spaced at 4'-0" centers. The transverse spacing of wheels shall be taken as 6'-0".

• For HS20-44 Truck, the design lane load shall consist of a load 640 lbs per linear foot, uniformly distributed in the longitudinal direction with a single concentrated load (or two concentrated loads in case of continuous spans for determination of maximum negative moment), so placed on the span as to produce maximum stress. The concentrated load and uniform load shall be considered as uniformly distributed over a 10'-0" width on a line normal to the center line of the lane.
• For HS20-44 Modified Truck, use the HS20-44 truck modified by a factor of 1.25.

• For the design of continuous structures, an additional concentrated load is placed in another span to create the maximum effect. For positive moments, only one concentrated load is used, combined with as many spans loaded uniformly as are required to produce the maximum moment.

26'-0" (up to 2 traffic lanes)
28'-0" (up to 2 traffic lanes)
30'-0" (up to 3 traffic lanes)
32'-0" (up to 3 traffic lanes)
36'-0" (up to 3 traffic lanes)
38'-0" (up to 3 traffic lanes)
40'-0" (up to 4 traffic lanes)
44'-0" (up to 4 traffic lanes)

#### 751.40.8.1.2 Impact

Highway live loads shall be increased by a factor given by the following formula:

${\displaystyle \,I={\frac {50}{L+125}}}$   ${\displaystyle \,L}$ in feet

For continuous spans, ${\displaystyle \,L}$ to be used in this equation for negative moments is the average of two adjacent spans at an intermediate bent or the length of the end span at an end bent. For positive moments, ${\displaystyle \,L}$ is the span length from center to center of support for the span under consideration.

Impact is never to be more than 30 percent. It is intended that impact be included as part of the loads transferred from superstructure to substructure but not in loads transferred to footings or parts of substructure that are below the ground line. The design of neoprene bearing pads also does not include impact in the design loads.

#### 751.40.8.1.3 Collision Force

Collision forces shall be applied to the barrier or railing in the design of the cantilever slab. A force of 10 kips is to be applied at the top of the standard barrier or railing. This force is distributed through the barrier or railing to the slab.

#### 751.40.8.1.4 Centrifugal Force

Structures on curves shall be designed for a horizontal radial force equal to the following percentage of the live load in all the lanes, without impact.

${\displaystyle \,C={\frac {6.68S^{2}}{R}}}$

Where:

 ${\displaystyle \,C}$ = the centrifugal force in percent of the live load ${\displaystyle \,S}$ = the design speed in miles per hour ${\displaystyle \,R}$ = the radius of the curve in feet

This force shall be applied at 6 feet above the centerline of the roadway with one design truck being placed in each lane in a position to create the maximum effect. Lane loads shall not be used in calculating centrifugal forces.

The effects of superelevation shall be taken into account.

#### 751.40.8.1.5 Lateral Earth Pressure

Structures which retain fills shall be designed for active earth pressures as

${\displaystyle \,P_{a}=0.5(\gamma K_{a})H^{2}}$

Where:

 ${\displaystyle \,P_{a}}$ = active earth pressure per length (lb/ft) ${\displaystyle \,\gamma }$ = unit weight of the back fill soil = 120 lb/ft³ ${\displaystyle \,K_{a}}$ = coefficient of active earth pressure as given by Rankine’s formula ${\displaystyle \,\gamma K_{a}}$ = ${\displaystyle \,p_{a}}$ = equivalent fluid pressure (lb/ft³)(*) ${\displaystyle \,H}$ = height of the back fill soil (ft)

Rankine's Formula

The coefficient of active earth pressure ${\displaystyle \,K_{a}}$ is:

${\displaystyle \,K_{a}=(cos\alpha ){\Bigg (}{\frac {cos\alpha -{\sqrt {cos^{2}\alpha -cos^{2}\phi }}}{cos\alpha +{\sqrt {cos^{2}\alpha -cos^{2}\phi }}}}{\Bigg )}}$

Where:

 ${\displaystyle \,\phi }$ = angle of internal friction of the backfill soil (*) ${\displaystyle \,\alpha }$ = the angle of incline of the backfill

If the backfill surface is level, angle a is zero and ${\displaystyle \,K_{a}}$ is:

${\displaystyle \,K_{a}={\frac {1-sin\phi }{1+sin\phi }}}$

(*) Use the internal friction angle indicated on the Bridge Memorandum. However, if the friction angle is not determined, use the minimum equivalent fluid pressure value, ${\displaystyle \,p_{a}}$ , of 45 lb/ft³ for bridges and retaining walls. For box culverts use a maximum of 60 lb/ft³ and a minimum of 30 lb/ft³ for fluid pressure.

An additional earth pressure shall be applied to all structures which have live loads within a distance of half the structure height. This additional force shall be equal to adding 2'-0" of fill to that presently being retained by the structure.

#### 751.40.8.1.6 Longitudinal Forces (Braking Forces)

A longitudinal force of 5% of the live load shall be applied to the structure. This load shall be 5% of the lane load plus the concentrated load for moment applied to all lanes and adjusted by the lane reduction factor. Apply this force at 6 feet above the top of slab and to be transmitted to the substructure through the superstructure.

Wind loads shall be applied to the structure regardless of length.

The pressure generated by wind load is:

${\displaystyle \,P=KV^{2}}$

Where:

 ${\displaystyle \,P}$ = wind pressure in pounds per square foot ${\displaystyle \,V}$ = design wind velocity = 100 miles per hour ${\displaystyle \,K}$ = 0.004 for wind load

Basic wind load (pressure) = 0.004 x (100)² = 40 lb/ft²

Transverse

A wind load of the following intensity shall be applied horizontally at right angles to the longitudinal axis of the structure.

• Trusses and Arches = 75 pounds per square foot = ${\displaystyle \,W_{t}}$
• Girders and Beams = 50 pounds per square foot (*) = ${\displaystyle \,W_{t}}$ (for plate girder lateral bracing check only)
• The total force shall not be less than 300 pounds per linear foot in the plane of windward chord and 150 pounds per linear foot in the plane of the leeward chord on truss spans, and not less than 300 pounds per linear foot on girder spans.

Forces transmitted to the substructure by the superstructure and forces applied directly to the substructure by wind load shall be as follows:

Forces from Superstructure: Wind on Superstructure

Transverse

A wind load of the following intensity shall be applied horizontally at right angles to the longitudinal axis of the structure.

• Trusses and Arches = 75 pounds per square foot = ${\displaystyle \,W_{t}}$
• Girders and Beams = 50 pounds per square foot (*) = ${\displaystyle \,W_{t}}$

(*) Use Wt = 60 lbs/ft² for design wind force on girders and beams If the column height on a structure is greater than 50 feet, where the height is the average column length from ground line to bottom of beam.

The transverse wind force for a bent will be:

${\displaystyle \,P=L\times H\times W_{t}}$

Where:

 ${\displaystyle \,L}$ = length in feet = the average of two adjacent spans for intermediate bents and half of the length of the end span for end bents. ${\displaystyle \,H}$ = the total height of the girders, slab, barrier or raling and any superelevation of the roadway, in feet ${\displaystyle \,W_{t}}$ = wind force per unit area in pounds per square foot

This transverse wind force will be applied at the top of the beam cap for the design of the substructure.

Longitudinal (**)

The standard wind force in the longitudinal direction shall be applied as a percentage of the transverse loading. Use approximately 25%.

 Truss and Arch Structures ${\displaystyle \,W_{I}}$ = 75 x 0.25 = approximately 20 lbs/ft² Girder Structures ${\displaystyle \,W_{I}}$ = 50 x 0.25 = approximately 12 lbs/ft²

The total longitudinal wind force ${\displaystyle \,P}$ will be:

${\displaystyle \,P=L\times H\times W_{I}}$

Where:

 ${\displaystyle \,L}$ = the overall bridge length in feet ${\displaystyle \,H}$ = the total height of the girders, slab, barrier or railing and anysuperelevation of the roadway, in feet ${\displaystyle \,W_{I}}$ = wind force per unit area in pounds per square foot

This longitudinal force is distributed to the bents based on their stiffness. (**)

The longitudinal wind force for the bent will be applied at the top of the beam cap for the design of the substructure.

Forces from Superstructure: Wind on Live Load

A force of 100 pounds per linear foot of the structure shall be applied transversely to the structure along with a force of 40 pounds per linear foot longitudinally. These forces are assumed to act 6 feet above the top of slab. The transverse force is applied at the bents based on the length of the adjacent spans affecting them. The longitudinal force is distributed to the bents based on their stiffness. (**)

Forces Applied Directly to the Substructure

The transverse and longitudinal forces to be applied directly to the substructure elements shall be calculated from an assumed basic wind force of 40 lbs/ft². This wind force per unit area shall be multiplied by the exposed area of each substructure member in elevation (use front view for longitudinal force and side view for transversely force, respectively). These forces are acting at the center of gravity of the exposed portion of the member.

A shape factor of 0.7 shall be used in applying wind forces to round substructure members.

When unusual conditions of terrain or the special nature of a structure indicates, a procedure other than the Standard Specification may be used subject to approval of the Structural Project Manager.

#### 751.40.8.1.8 Temperature Forces

Temperature stresses or movement need to be checked on all structures regardless of length. Generation of longitudinal temperature forces is based on stiffness of the substructure. (*)

Coefficients

 Steel: Thermal - 0.0000065 ft/ft/°F Concrete: Thermal - 0.0000060 ft/ft/°F Shrinkage - 0.0002 ft/ft (***) Friction - 0.65 for concrete on concrete

 Rise Fall Range Steel Structures 60°F 80°F 140°F Concrete Structures 30°F 40°F 70°F

(**) Temperature Range for expansion bearing design and expansion devices design see EPG 751.11 Bearings and EPG 751.13 Expansion Devices, respectively.

(***) When calculating substructure forces of concrete slab bridges, the forces caused by the shrinkage of the superstructure should be included with forces due to temperature drop. This force can be ignored for most other types of bridges.

Sidewalk floors and their immediate support members shall be designed for a live load of 85 pounds per square foot of sidewalk area. Girders, trusses, and other members shall be design for the following sidewalk live load:

 Spans 0 to 25 feet 85 lbs/ft² Spans 26 to 100 feet 60 lbs/ft² Spans over 100 feet use the following formula

${\displaystyle \,P={\Bigg (}30+{\frac {3000}{L}}{\Bigg )}{\Bigg (}{\frac {55-W}{50}}{\Bigg )}}$

Where:

 ${\displaystyle \,P}$ = live load per square foot, max. 60 lbs/ft² ${\displaystyle \,L}$ = loaded length of sidewalk in feet ${\displaystyle \,W}$ = width of sidewalk in feet

When sidewalk live loads are applied along with live load and impact, if the structure is to be designed by service loads, the allowable stress in the outside beam or stringer may be increased by 25 percent as long as the member is at least as strong as if it were not designed for the additional sidewalk load using the initial allowable stress. When the combination of sidewalk live load and traffic live load plus impact governs the design under the load factor method, use a b factor of 1.25 instead of 1.67.

Unless a more exact analysis can be performed, distribution of sidewalk live loads to the supporting stringers shall be considered as applied 75 percent to the exterior stringer and 25 percent to the next stringer.

Stream Pressure

Stream flow pressure shall be considered only in extreme cases. The affect of flowing water on piers shall not be considered except in cases of extreme high water and when the load applied to substructure elements is greater than that which is applied by wind on substructure forces at low water elevations.

The pressure generated by stream flow is:

${\displaystyle \,P=KV^{2}}$

Where:

 ${\displaystyle \,P}$ = stream pressure in pounds per square foot ${\displaystyle \,V}$ = design velocity of water in feet per second ${\displaystyle \,K}$ = shape constant for the surface the water is in contact with. ${\displaystyle \,K}$ = 1.4 for square-ended piers ${\displaystyle \,K}$ = 0.7 for circular piers ${\displaystyle \,K}$ = 0.5 for angle-ended piers where the angle is 30 degrees or less

Ice Forces

Ice forces on piers shall be applied if they are indicated on the Bridge Memorandum.

Buoyancy

Buoyancy shall be considered when its effects are appreciable.

Fatigue in Structural Steel

Prestressing

Other loads may need to be applied if they are indicated on the Bridge Memorandum. Otherwise see Structural Project Manager before applying any additional loads.

 GP I SL ${\displaystyle \,=D+L+I}$ 100% GP II SL ${\displaystyle \,=D+W}$ 125% GP III SL ${\displaystyle \,=D+L+I+0.3W+WL+LF}$ 125% GP IV SL ${\displaystyle \,=D+L+I+T}$ 125% GP V SL ${\displaystyle \,=D+W+T}$ 140% GP VI SL ${\displaystyle \,=D+L+I+0.3W+WL+LF+T}$ 140%

Where:

 ${\displaystyle \,D}$ = dead load ${\displaystyle \,L}$ = live load ${\displaystyle \,I}$ = live load impact ${\displaystyle \,W}$ = wind load on structure ${\displaystyle \,WL}$ = wind load on live load ${\displaystyle \,T}$ = temperature force ${\displaystyle \,LF}$ = longitudinal force from live load

 GP I LF ${\displaystyle \,=1.3[\beta _{d}D+1.67(L+I)]}$ GP II LF ${\displaystyle \,=1.3[\beta _{d}D+W]}$ GP III LF ${\displaystyle \,=1.3[\beta _{d}D+L+I+0.3W+WL+LF]}$ GP IV LF ${\displaystyle \,=1.3[\beta _{d}D+L+I+T]}$ GP V LF ${\displaystyle \,=1.25[\beta _{d}D+W+T]}$ GP VI LF ${\displaystyle \,=1.25[\beta _{d}D+L+I+0.3W+WL+LF+T]}$

Where:

 ${\displaystyle \,D}$ = dead load ${\displaystyle \,L}$ = live load ${\displaystyle \,I}$ = live load impact ${\displaystyle \,W}$ = wind load on structure ${\displaystyle \,WL}$ = wind load on live load ${\displaystyle \,T}$ = temperature force ${\displaystyle \,LF}$ = longitudinal force from live load ${\displaystyle \,\beta _{d}}$ = coefficient, see AASHTO Table 3.22.1A

Other group loadings in AASHTO Table 3.22.1A shall be used when they apply.

Composite Steel or Prestressed Concrete Structures

The dead load applied to the girders through the slab shall be:

Non-composite dead loads should be distributed to girders (stringers) on the basis of continuous spans over simple supports.

Barrier or railing
Future wearing surface on slab
Sidewalks
Fences
Protective coatings and waterproofing on slab

Concrete Slab Bridges

For longitudinal design, heavier portions of the slab may be considered as concentrated load for entry into the "Continuous Structure Analysis" computer program.

For transverse bent design, consider the dead load reaction at the bent to be a uniform load across entire length of the transverse beam.

#### 751.40.8.2.2 Distribution of Live Load

Superstructure

For application of live load to superstructure, the lane width is considered 12 feet. Each design vehicle has wheel lines which are 6 feet apart and adjacent design vehicles must be separated by 4 feet.

Substructure

To produce the maximum stresses in the main carrying members of substructure elements, multiple lanes are to be loaded simultaneously. The lane width is 12 feet. Partial lanes are not to be considered. Due to the improbability of coincident maximum loading, a reduction factor is applied to the number of lanes. This reduction however, is not applied in determining the distribution of loads to the stringers.

Distribution of Live Load to Beams and Girders
Number of Lanes Percent
one or two lanes 100
three lanes 90
four lanes or more 75

Moment Distribution

Moments due to live loads shall not be distributed longitudinally. Lateral distribution shall be determined from AASHTO Table 3.23.1 for interior stringers. Outside stringers distribute live load assuming the flooring to act as a simple span, except in the case of a span with a concrete floor supported by four or more stringers, then AASHTO 3.23.2.3.1.5 shall be applied. In no case shall an exterior stringer have less carrying capacity than an interior stringer.

Shear Distribution

As with live load moment, the reactions to the live load are not to be distributed longitudinally. Lateral distribution of live load shall be that produced by assuming the flooring to act as simply supported. Wheel lines shall be spaced on accordance with AASHTO 3.7.6 and shall be placed in a fashion which provides the most contribution to the girder under investigation, regardless of lane configuration. The shear distribution factor at bents shall be used to design bearings and bearing stiffeners.

Deflection Distribution

Deflection due to live loads shall not be distributed longitudinally. Lateral distribution shall be determined by averaging the moment distribution factor and the number of wheel lines divided by the number of girder lines for all girders. The number of wheel lines shall be based on 12 foot lanes. The reduction in load intensity (AASHTO Article 3.12.1) shall not be applied.

Deflection Distribution Factor =   ${\displaystyle \,{\cfrac {{\big \{}{\frac {2n}{N}}{\big \}}+MDF}{2}}}$

Where:

 ${\displaystyle \,n}$ = number of whole 12 foot lanes on the roadway ${\displaystyle \,N}$ = number of girder lines; ${\displaystyle \,MDF}$ = Moment Distribution Factor.

Example: 38'-0" Roadway (Interior Girder),   ${\displaystyle \,n=3}$,   ${\displaystyle \,N=5}$,   ${\displaystyle \,MDF=1.576}$

Deflection Distribution Factor =   ${\displaystyle \,{\cfrac {{\big \{}{\frac {2\times 3lanes}{5girders}}{\big \}}+1.576}{2}}=1.388}$

Width
Number
Girders
Girder
Spacing
Exterior Girder Interior Girder (1)
Mom. Shear Defl. Mom. Shear Defl.
26’-0” 4 7’-6” 1.277 1.133 1.139 1.364 1.667 1.182 1.071
28’-0” 4 8’-2” 1.352 1.204 1.176 1.485 1.776 1.243 1.167
30’-0” 4 8’-8” 1.405 1.308 1.453 1.576 1.846 1.538 1.238
32’-0” 4 9’-2” 1.457 1.400 1.479 1.667 1.909 1.584 1.310
36’-0” 5 8’-2” 1.352 1.184 1.276 1.485 1.776 1.343 1.167
38’-0” 5 8’-8” 1.405 1.231 1.303 1.576 1.846 1.388 1.238
40’-0” 5 9’-0” 1.440 1.333 1.520 1.636 1.889 1.618 1.286
44’-0” 5 9’-9” 1.515 1.487 1.558 1.773 1.974 1.687 1.393

Distribution of Live Load to Substructure

For substructure design the live load wheel lines shall be positioned on the slab to produce maximum moments and shears in the substructure. The wheel lines shall be distributed to the stringers on the basis of simple spans between stringers. The number of wheel lines used for substructure design shall be based on 12 foot lanes and shall not exceed the number of lanes times two with the appropriate percentage reduction for multiple lanes where applicable.

In computing these stresses generated by the lane loading, each 12 foot lane shall be considered a unit. Fractional units shall not be considered.

For simple spans, the span length shall be the distance center to center of supports but need not be greater than the clear distance plus the thickness of the slab. Slabs for girder and floor beam structures should be designed as supported on four sides.

For continuous spans on steel stringers or on thin flanged prestressed beams (top flange width to thickness ratios > 4.0), the span length shall be the distance between edges of top flanges plus one quarter of each top flange width. When the top flange width to thickness is < 4.0 the span distance shall be the clear span between edges of the top flanges.

When designing the slab for live load, the wheel line shall be placed 1 foot from the face of the barrier or railing if it produces a greater moment.

Bending Moments in Slab on Girders

The load distributed to the stringers shall be:

${\displaystyle \,{\Bigg (}{\frac {S+2}{32}}{\Bigg )}}$   P20 or P25 = Moment in foot-pounds per-foot width of slab.

Where:

 ${\displaystyle \,S}$ = effective span length between girders in feet P20 or P25 = wheel line load for HS20 or HS20 Modified design Truck in kips.

For slabs continuous over 3 or more supports, a continuity factor of 0.8 shall be applied.

Main Reinforcement Parallel to Traffic

This distribution may be applied to special structure types when its use is indicated.

Distribution of Live Load to Concrete Slab Bridges

Live load for transverse beam, column and pile cap design shall be applied as concentrated loads of one wheel line. The number of wheel lines used shall not exceed the number of lanes x 2 with the appropriate reduction where applicable.

For slab longitudinal reinforcement design, use live load moment distribution factor of 1/E for a one-foot strip slab with the appropriate percentage reduction.

${\displaystyle \,E=4'+0.06S,E(max.)=7'}$

Where:

 ${\displaystyle \,E}$ = Width of slab in feet over which a wheel is distributed ${\displaystyle \,S}$ = Effective span length in feet.

For slab deflection, use the following deflection factor for a one-foot strip slab without applying percentage reduction.

Deflection Factor = (Total number of wheel line) / (width of the slab)

#### 751.40.8.2.3 Frictional Resistance

The frictional resistance varies with different surfaces making contact. In the design of bearings, this resistance will alter how the longitudinal forces are distributed. The following table lists commonly encountered materials and their coefficients. These coefficients may be used to calculate the frictional resistance at each bent.

Frictional Resistance of Expansion Bearings
Bearing Type Coef. General Data
Type C Bearing 0.14 Coef. of sliding friction
steel to steel = 0.14

Coef. for pin and rocker
type bearing =

${\displaystyle \,{\frac {0.14(Radius\ of\ pin)}{Radius\ of\ Rocker}}}$

Frictional Force =
Reaction x Coef.

6” Diameter Roller 0.01
Type D Bearing
2” 6.5” 0.0216
2” 7” 0.0200
2” 7.5” 0.0187
2” 8” 0.0175
2” 10.5” 0.0133
PTFE Bearing 0.0600

The design of a bent with one of the above expansion bearings will be based on the maximum amount of load the bearing can resist by static friction. When this static friction is overcome, the longitudinal forces are redistributed to the other bents.

The maximum static frictional force at a bent is equal to the sum of the forces in each of the bearings. The vertical reaction used to calculate this maximum static frictional force shall be Dead Loads only for all loading cases. Since the maximum longitudinal load that can be experienced by any of the above bearings is the maximum static frictional force, the effects of longitudinal wind and temperature can not be cumulative if their sum is greater than this maximum static frictional force.

Two conditions for the bents of the bridge are to be evaluated.

1. Consider the expansion bents to be fixed and the longitudinal loads distributed to all of the bents.
2. When the longitudinal loads at the expansion bearings are greater than the static frictional force, then the longitudinal force of the expansion bearings is equal to the dynamic frictional force. It is conservative to assume the dynamic frictional force to be zero causing all longitudinal loads to be distributed to the remaining bents.

### 751.40.8.3 Unit Stresses

#### 751.40.8.3.1 Fatigue in Structural Steel

AADTT, annual average daily truck traffic (one direction), shall be indicated on the Bridge Memorandum. Based on AADTT, the fatigue case and corresponding stress cycles can be obtained from AASHTO Table 10.3.2A.

When Case I fatigue is considered, it is necessary to check fatigue due to truck loading for both the 2,000,000 and over 2,000,000 stress cycles. For the over 2,000,000 stress cycles, the moment distribution factor for all stringers or girders (for fatigue stresses only) will be based on one lane loaded. For truck loading 2,000,000 cycles and lane loading 500,000 cycles, use the moment distribution factor based on two or more traffic lanes (same as for design moment).

The number of cycles to be used in the fatigue design is dependent on the case number and type of load producing maximum stress as indicated in AASHTO Table 10.3.2A. The allowable fatigue stress range based on the fatigue stress cycles can be obtained from AASHTO Table 10.3.1A.

The type of live load used to determine the number of cycles will be the type of loading used to determine the maximum stress at the point under consideration.

Only live loading and impact stresses need to be considered when designing for fatigue.

Fatigue criteria applies only when the stress range is one of tension to tension or reversal. The fatigue criteria does not apply to the stress range from compression to compression.

All fracture critical structures, those which consist of only one or two main carrying members, trusses or single box girders, shall be considered as Non-redundant structures. Use the appropriate table which accompanies these structures.

#### 751.40.8.3.2 Reinforced Concrete

Allowable Stresses of Reinforcing Steel

Tensile stress in reinforcement at service loads, ${\displaystyle \,f_{s}}$:

Concrete
Reinforcing Steel (Grade 40) ${\displaystyle \,f_{s}}$ = 20,000 psi
Reinforcing Steel (Grade 60) ${\displaystyle \,f_{s}}$ = 24,000 psi

For compression stress in beams, see AASHTO Article 8.15.3.5.

For compression stress in columns, see AASHTO Article 8.15.4.

For fatigue stress limit, see AASHTO Article 8.16.8.3.

Fatigue in Reinforcing Steel

For flexural members designed with reference to load factors and strengths by Strength Design Method, stresses at service load shall be limited to satisfy the requirements for fatigue. Reinforcement should be checked for fatigue at all locations of peak service load stress ranges and at bar cut-off locations except for concrete deck slab in multi-girder applications.

Allowable Stress Range: ${\displaystyle \,fr_{allow}}$

The allowable stress range is found using the equation listed below and the minimum stresses from dead load, live load, and impact based on service loads.

The term minimum stress level fmin for this formula indicates the algebraic minimum stress level: tension stress with a positive sign and compression stress with a negative sign.

${\displaystyle \,fr_{allow}=21-0.33f_{min}+8(r/h)}$

Where:

 ${\displaystyle \,fr_{allow}}$ = allowable stress range (ksi) ${\displaystyle \,f_{min}}$ = algebraic minimum stress level ksi): positive if tension, negative if compression. ${\displaystyle \,r/h}$ = ratio of base radius to height of rolled-on transverse deformation; if the actual value is not know, 0.3 may be used. ${\displaystyle fr_{allow}}$ = ${\displaystyle \,23.4-0.33f_{min}}$     when ${\displaystyle \,r/h=0.3}$

Fatigue research has shown that increasing minimum tensile stress results in a decrease in fatigue strength for a tension to tension stresses case. The fatigue strength increases with a bigger compressive stress in a tension to compression stresses case.

Actual Stress Range: ${\displaystyle \,fr_{act}}$

The actual stress range, ${\displaystyle \,fr_{act}}$, is found using dead load, live load, and impact from service loads.

 ${\displaystyle \,fr_{act}}$ = ${\displaystyle \,f_{GT}-f_{LT}}$ ${\displaystyle \,f_{GT}}$ = greatest tension stress level (ksi), always positive. (Not necessary to check compression to compression for fatigue.) ${\displaystyle \,f_{LT}}$ = algebraic least stress level (ksi): ${\displaystyle \,f_{LT}}$ = positive if the least stress is tension (tension to tension stresses) ${\displaystyle \,f_{L}T}$ = negative if the least stress is compression (tension to compression stresses)

Tension and Compression Stress Computation

Tension and compression stress are determined by using the following formulae for double reinforced concrete rectangular beams.

${\displaystyle \,f_{s}}$ = tensile stress in reinforcement at service loads (ksi)

Tensile stress   ${\displaystyle \,f_{s}={\frac {M}{A_{s}jd}}}$

${\displaystyle \,f'_{s}}$ = compressive stress in reinforcement at service loads (ksi)

Compressive stress   ${\displaystyle \,f'_{s}={\frac {M}{A_{s}jd}}{\Bigg (}{\cfrac {k-{\frac {d^{1}}{d}}}{1-k}}{\Bigg )}}$

Where:

${\displaystyle \,j={\cfrac {k^{2}{\Big (}1-{\frac {k}{c}}{\Big )}+2\rho 'n{\Big (}k-{\frac {d'}{d}}{\Big )}{\Big (}1-{\frac {d'}{d}}{\Big )}}{k^{2}+2\rho 'n{\Big (}k-{\frac {d'}{d}}{\Big )}}}}$      Eq. 2.2-1

${\displaystyle \,k={\sqrt {2n{\Bigg (}\rho +\rho '{\Bigg (}{\frac {d'}{d}}{\Bigg )}{\Bigg )}+n^{2}{\big (}\rho +\rho '{\big )}^{2}-n{\big (}\rho +\rho '{\big )}}}}$      Eq. 2.2-2

 ${\displaystyle \,\rho }$ = tension reinforcement ratio,   ${\displaystyle \,\rho ={\frac {A_{s}}{bd}}}$ ${\displaystyle \,\rho '}$ = compression reinforcement ratio,   ${\displaystyle \,\rho '={\frac {A'_{s}}{bd}}}$ ${\displaystyle \,A_{s}}$ = area of tension reinforcement (sq. inch) ${\displaystyle \,A'_{s}}$ = area of compression reinforcement (sq. inch) ${\displaystyle \,b}$ = width of beam (inch) ${\displaystyle \,d}$ = distance from extreme compression fiber to centroid of tension reinforcement (inch) ${\displaystyle \,d'}$ = distance from extreme compression fiber to centroid of compression reinforcement (inch) ${\displaystyle \,jd}$ = distance from tensile steel to resultant compression (inch) ${\displaystyle \,kd}$ = distance from neutral plane to compression surface (inch) ${\displaystyle \,n}$ = ratio of modulus of elasticity of steel to that of concrete

### 751.40.8.4 Standard Details

#### 751.40.8.4.1 Welding Details

All welding shall be detailed in accordance with ANSI / AASHTO / AWS D1.5, Bridge Welding Code.

For ASTM A709, Grade 36 steel (Service Load Design ${\displaystyle \,F_{u}}$ = 58,000 psi) the allowable shear stress in fillet welds (${\displaystyle \,F_{V}}$) is:

${\displaystyle \,F_{V}=0.27F_{u}}$

Where:

 ${\displaystyle \,F_{V}}$ = allowable basic shear stress ${\displaystyle \,F_{u}}$ = tensile strength of the electrode classification but not greater than the tensile strength of the connected part

 Size of Fillet Weld(Inch) Allowable Shear Loads per Length(Pound per lineal inch) 1/8” 1,380 3/16” 2,075 1/4" 2,770 5/16” 3,460 3/8” 4,150 1/2" 5,535 5/8” 6,920 3/4" 8,300 7/8” 9,690 1” 11,070

(*) Allowable Shear Load = ${\displaystyle \,(0.27)(58000psi)(0.707xSizeofWeld)(L)}$

Where:

 ${\displaystyle \,L}$ = Effective Length, in inch ${\displaystyle \,(0.707xSizeofWeld)}$ = Effective Throat, in inch ${\displaystyle \,(0.707xSizeofWeld)(L)}$ = Effective weld area in sq. inch

#### 751.40.8.4.2 Development and splicing of Reinforcement

##### 751.40.8.4.2.1 General

Development of Tension Reinforcement

Development lengths for tension reinforcement shall be calculated in accordance with AASHTO Article 8.25. Development length modification factors described in AASHTO Articles 8.25.3.2 and 8.25.3.3 shall only be used in situations where development length without these factors is difficult to attain. All other modification factors shown shall be used.

Development lengths for tension reinforcement have been tabulated on the following pages and include the modification factors except those described above.

Lap Splices of Tension Reinforcement

Lap splices of reinforcement in tension shall be calculated in accordance with AASHTO Article 8.32.1 and 8.32.3. Class C splices are preferred when possible, however it is permissible to use Class A or B when physical space is limited. The designer shall satisfy AASHTO Table 8.32.3.2 when using Class A or B splices. It should be noted that As required is based on the stress encountered at the splice location, which is not necessarily the maximum stress used to design the reinforcement.

Temperature and shrinkage reinforcement is assumed to fully develop the specified yield stresses. Therefore the development length shall not be reduced by (${\displaystyle \,A_{s}}$ required)/(${\displaystyle \,A_{s}}$ supplied).

Splice lengths for tension reinforcement have been tabulated on the following pages and include the development length modifications as described above.

Development of Tension Hooks

Development of tension hooks shall be calculated in accordance with AASHTO Article 8.29. Hook length modification factors described in Articles 8.29.3.3 and 8.29.3.4 shall only be used in situations where hook length without these factors is difficult to attain. All other modification factors shown shall be used.

Development lengths of tension hooks have been tabulated on the following pages and include the modification factors except those described above.

Development of Compression Reinforcement

Development lengths for compression reinforcement shall be calculated in accordance with AASHTO Article 8.26. Development length modification factors described in AASHTO Articles 8.26.2.1 and 8.26.2.2 shall only be used in situations where development length without these factors is difficult to attain. All other modification factors shown shall be used.

Development lengths for compression reinforcement have been tabulated on the following pages and include the modification factors except those described above.

Lap Splices of Compression Reinforcement

Lap splices of reinforcement in compression shall be calculated in accordance with AASHTO Article 8.32.1 and 8.32.4.

Splice lengths for compression reinforcement have been tabulated on the following pages.

Mechanical Bar Splices

Mechanical bar splices may be used in situations where it is not possible or feasible to use lap splices. Mechanical bar splices shall meet the criteria of AASHTO Article 8.32.2. Refer to the manufacturers literature for more information on the design of mechanical bar splices.

##### 751.40.8.4.2.2 Development and Tension Lap Splice Lengths - Top Bars (${\displaystyle \,F_{y}}$ = 60 ksi)

Top reinforcement is placed so that more than 12” of concrete is cast below the reinforcement.

Class A splice =1.0 ${\displaystyle \,L_{d}}$, Class B splice =1.3 ${\displaystyle \,L_{d}}$, Class C splice =1.7 ${\displaystyle \,L_{d}}$

Use development and tension lap splices of ${\displaystyle \,f'_{c}}$ = 4 ksi for concrete strengths greater than 4 ksi.

##### 751.40.8.4.2.3 Development and Tension Lap Splice Lengths - Other Than Top Bars (${\displaystyle \,F_{y}}$ = 60 ksi)

Class A splice =1.0 ${\displaystyle \,L_{d}}$, Class B splice =1.3 ${\displaystyle \,L_{d}}$, Class C splice =1.7 ${\displaystyle \,L_{d}}$

Use development and tension lap splices of ${\displaystyle \,f'_{c}}$ = 4 ksi for concrete strengths greater than 4 ksi.

##### 751.40.8.4.2.4 Development and Lap Splice Lengths - Bars in Compression (${\displaystyle \,F_{y}}$ = 60 ksi)

Development length for spirals, ${\displaystyle \,L_{d}}$, ${\displaystyle \,_{spiral}}$, should be used if reinforcement is enclosed in a spiral of not less than 1/4” diameter and no more than 4” pitch. See AASHTO 8.26 for special conditions.

All values are for splices with the same size bars. For different size bars, see AASHTO 8.32.4.

(*) Lap splices for #14 and #18 bars are not permitted except as column to footing dowels.

##### 751.40.8.4.2.5 Development of Standard Hooks in Tension, Ldh (${\displaystyle \,F_{y}}$ = 60 ksi)

The development length, ${\displaystyle \,L_{dh}}$, is measured from the critical section to the outside edge of hook. The tabulated values are valid for both epoxy and uncoated hooks.

Case A - For #11 bar and smaller, side cover (normal to plane of hook) less than 2 1/2 inches and for a 90 degree hook with cover on the hook extension less than 2 inches.

Case B - For #11 bar and smaller, side cover (normal to plane of hook) greater than 2 1/2 inches and for a 90-dgree hook with cover on the hook extension 2 inches or greater.

(*) See Structural Project Manager before using #14 or #18 hook.

DETAILS NEAR FREE EDGEOR CONSTRUCTION JOINT (1) = ${\displaystyle \,4d_{b}}$ (#3 thru #8) (1) = ${\displaystyle \,5d_{b}}$ (#9, #10 and #11) (1) = ${\displaystyle \,6d_{b}}$ (#14 and #18)
##### 751.40.8.4.2.6 Development of Uncoated Grade 40 Deformed Bars in Tension, ${\displaystyle \,L_{d}}$ (AASHTO 8.25)
Bars spaced laterally less than 6 inches on center or less than 3 inches concrete cover in direction of the spacing
Bar ${\displaystyle \,f'_{c}}$ = 3 ksi ${\displaystyle \,f'_{c}}$ = 4 ksi ${\displaystyle \,f'_{c}}$ = 5 ksi
${\displaystyle \,L_{d}}$ ${\displaystyle \,L_{d}}$ Top bar ${\displaystyle \,L_{d}}$ ${\displaystyle \,L_{d}}$ Top bar ${\displaystyle \,L_{d}}$ ${\displaystyle \,L_{d}}$ Top bar
#3 12 12 12 12 12 12
#4 12 12 12 12 12 12
#5 12 14 12 14 12 14
#6 13 19 12 17 12 17
#7 18 25 16 22 14 20
#8 23 33 20 28 18 25
#9 30 41 26 36 23 32
#10 38 52 33 45 29 41
#11 46 64 40 56 36 50
#14 63 87 54 76 49 68
#18 81 113 70 98 63 88

Bars spaced laterally 6 inches or more on center and at least 3 inches concrete cover in direction of the spacing
Bar ${\displaystyle \,f'_{c}}$ = 3 ksi ${\displaystyle \,f'_{c}}$ = 4 ksi ${\displaystyle \,f'_{c}}$ = 5 ksi
${\displaystyle \,L_{d}}$ ${\displaystyle \,L_{d}}$ Top bar ${\displaystyle \,L_{d}}$ ${\displaystyle \,L_{d}}$ Top bar ${\displaystyle \,L_{d}}$ ${\displaystyle \,L_{d}}$ Top bar
#3 12 12 12 12 12 12
#4 12 12 12 12 12 12
#5 12 12 12 12 12 12
#6 12 15 12 14 12 14
#7 15 20 13 18 12 16
#8 19 26 16 23 15 20
#9 24 33 21 29 19 26
#10 30 42 26 36 23 33
#11 37 52 32 45 29 40
#14 50 70 44 61 39 54
#18 65 90 56 78 50 70
##### 751.40.8.4.2.7 Minimum lap length for uncoated Grade 40 tension lap splices, ${\displaystyle \,L_{lap}}$ (AASHTO 8.32)
Bars spaced less than 6 inches laterally on center and at least 3 inches concrete cover in direction of the spacing
Other than Top Bars Top Bars
${\displaystyle \,f'_{c}}$ = 3 ksi ${\displaystyle \,f'_{c}}$ = 4 ksi ${\displaystyle \,f'_{c}}$ = 5 ksi ${\displaystyle \,f'_{c}}$ = 3 ksi ${\displaystyle \,f'_{c}}$ = 4 ksi ${\displaystyle \,f'_{c}}$ = 5 ksi
Bar A B C A B C A B C A B C A B C A B C
#3 12 12 12 12 12 12 12 12 12 12 16 21 12 16 21 12 16 21
#4 12 12 14 12 12 14 12 12 14 12 16 21 12 16 21 12 16 21
#5 12 13 17 12 13 17 12 13 17 14 19 24 14 19 24 14 19 24
#6 13 17 22 12 16 21 12 16 21 19 24 31 17 22 29 17 22 29
#7 18 23 30 16 20 26 14 19 24 25 32 42 22 28 37 20 26 34
#8 23 30 40 20 26 34 18 24 31 33 42 55 28 37 48 25 33 43
#9 30 38 50 26 33 43 23 30 39 41 54 70 36 47 61 32 42 54
#10 38 49 63 33 42 55 29 38 49 52 68 89 45 59 77 41 53 69
#11 46 60 78 40 52 68 36 46 61 64 84 109 56 72 95 50 65 85

Bars spaced 6 inches or more laterally on center and at least 3 inches concrete cover in direction of the spacing
Other than Top Bars Top Bars
${\displaystyle \,f'_{c}}$ = 3 ksi ${\displaystyle \,f'_{c}}$ = 4 ksi ${\displaystyle \,f'_{c}}$ = 5 ksi ${\displaystyle \,f'_{c}}$ = 3 ksi ${\displaystyle \,f'_{c}}$ = 4 ksi ${\displaystyle \,f'_{c}}$ = 5 ksi
Bar A B C A B C A B C A B C A B C A B C
#3 12 12 12 12 12 12 12 12 12 12 16 21 12 16 21 12 16 21
#4 12 12 12 12 12 12 12 12 12 12 16 21 12 16 21 12 16 21
#5 12 12 14 12 12 14 12 12 14 12 16 21 12 16 21 12 16 21
#6 12 14 18 12 13 17 12 13 17 15 19 25 14 18 23 14 18 23
#7 15 19 24 13 16 21 12 15 20 20 26 34 18 23 29 16 21 27
#8 19 24 32 16 21 28 15 19 25 26 34 44 23 29 38 20 26 34
#9 24 31 40 21 27 35 19 24 31 33 43 56 29 37 49 26 33 44
#10 30 39 51 26 34 44 23 30 39 42 54 71 36 47 62 33 42 55
#11 37 48 63 32 42 54 29 37 49 52 67 87 45 58 76 40 52 68

#### 751.40.8.4.3 Miscellaneous

Negative Moment Steel over Intermediate Supports

Dimension negative moment steel over intermediate supports as shown.

Prestressed Structures:
(1) Bar length by design.
(2) Reinforcement placed between longitudinal temperature reinforcing in top.
 Bar size: #5 bars at 7-1/2" cts. (Min.) #8 bars at 5" cts. (Max.)
Steel Structures:
(1) Extend into positive moment region beyond "Anchor" Stud shear connectors at least 40 x bar diameter x 1.5 (Epoxy Coated Factor)(*) as shown below. (AASHTO 10.38.4.4 & AASHTO 8.25.2.3)
(2) Use #6 bars at 5" cts. between longitudinal temperature reinforcing in top.
 (*) 40 x bar diameter x 1.5 = 40 x 0.75" x 1.5 = 45” for #6 epoxy coated bar.

### 751.40.8.5 General Superstructure

#### 751.40.8.5.1 Concrete Slabs

##### 751.40.8.5.1.1 Design Criteria

Slabs on Girders

Stresses:

 ${\displaystyle \,f_{c}}$ = 1,600 psi ${\displaystyle \,f'_{c}}$ = 4,000 psi ${\displaystyle \,n}$ = 8 ${\displaystyle \,f_{y}}$ = 60,000 psi

Moments Over Interior Support (Use for positive moment reinf. also) (Sec. 1.5 E40A)

 Dead Load = ${\displaystyle \,-0.107wS^{2}}$ (Continuous over 5 supports) Dead Load = ${\displaystyle \,-0.100wS^{2}}$ (Continuous over 4 supports)
 Live Load = ${\displaystyle \,(S+2){\frac {P}{32}}}$ Continuity Factor = 0.8 Impact Factor = 1.3 P = 16 Kips for HS20 P = 20 Kips for HS20 Modified Design Load: ${\displaystyle \,M_{u}=1.3(M_{DL}+1.67M_{LL+I})}$

Cantilever Moment

Wheel Load =   ${\displaystyle \,M_{LL=I}={\frac {Px}{E}}}$

Where:

 ${\displaystyle \,P}$ = Wheel load (apply impact factor) ${\displaystyle \,x}$ = Distance from load to support (ft.) ${\displaystyle \,E}$ = ${\displaystyle \,0.8x+3.75}$

Collision Load =   ${\displaystyle M_{COLL}={\frac {Py}{E}}}$

Where:

 ${\displaystyle \,P}$ = 10 kips (Collision force) ${\displaystyle \,y}$ = Moment arm (Curb ht.+ 1/2 Slab th.) ${\displaystyle \,E}$ = ${\displaystyle \,0.8x+5.0}$

Where:

 ${\displaystyle \,x}$ = Distance from center of gravity of barrier to support

 The "support" is assumed at the 1/4 point of the minimum flange. Wheel loads and collision loads shall not be applied simultaneously. Use the greater of the two for the Design Load. Design Load:${\displaystyle \,M_{u}=1.3(M_{DL}+1.67M_{LL+I})}$

Design of top reinforcement is based on maximum moment over supports or cantilever moment. Flexural reinforcement shall meet the criteria of AASHTO Art. 8.16.3.

When designing for bottom transverse reinforcement, a 1" wearing surface is removed from the effective depth.

Prestressed panels replace the bottom transverse reinforcement.

Prestressed panels are assumed to carry DL1 stresses. Therefore, the negative moment due to DL1 at interior supports may be neglected.

The maximum P/S panel width (clear span + 6") for HS20 Modified is 9'-6". (Based on 10'-0" girder spacing and 10" flanges) The maximum P/S panel width (clear span + 6") for HS20 is 9'-11".

Distribution of Flexural Reinforcement

Allowable Stress:   ${\displaystyle \,f_{s}={\frac {Z}{(d_{c}\times A)^{1/3}}}\leq 0.6f_{y}}$

Where:

 ${\displaystyle \,Z}$ = 130 k/in. ${\displaystyle \,d_{c}}$ = Dist. from extreme tension fiber to center of closest bar (concrete cover shalll not be taken greater than 2") ${\displaystyle \,A}$ = Effective tension area of concrete = ${\displaystyle \,2d_{c}s}$ ${\displaystyle \,s}$ = Bar spacing ctr. to ctr.

Actual Stress:   ${\displaystyle \,f_{s}={\frac {M_{W}}{A_{S}\times j\times d}}}$

Where:

 ${\displaystyle \,M_{W}}$ = Service load moment ${\displaystyle \,A_{S}}$ = Area of steel ${\displaystyle \,j}$ = ${\displaystyle \,1-k/3}$ ${\displaystyle \,k}$ = ${\displaystyle \,{\sqrt {2n\rho +(n\rho )^{2}-n\rho }}}$ ${\displaystyle \,n}$ = ${\displaystyle \,E_{S}/E_{C}}$ ${\displaystyle \,\rho }$ = ${\displaystyle \,A_{S}/(b\times d)}$ ${\displaystyle \,b}$ = Effective width ${\displaystyle \,d}$ = Effective depth

Distribution of flexural reinforcement does not need to be checked in concrete considered unexposed to weather.

Longitudinal distribution reinforcement:

Top of slab - use #5 bars at 15" cts. for temperature distribution.

Bottom of slab - by design.

Negative moment reinforcement over supports:

Steel structures - add. #6 bars at 5" between #5 bars.

P/S girder structures - by design.

Additional reinforcement over supports shall be a minimum of #5 bars and a maximum of #8 bars at 5" ctrs. When necessary, replace the #5 temperature reinforcement with a larger bar to satisfy negative moment reinforcement requirement, but keep all bars within two bar sizes.

Note: See details of negative moment reinforcement.

 3" Cl. preferred min., 2 3/4" Cl. preferred min. for P/S panels to accommodate #8 bars over supports and 2 1/2" Cl. absolute min. by AASHTO 8.22.1.

Method of measurement:

The area of the concrete slab shall be measured and computed to the nearest square yard. This area shall be measured transversely from out to out of slab and longitudinally from end to end of bridge slab.

Precast Prestressed Panels

3" Precast prestressed concrete panels with 5-1/2" minimum cast-in-place concrete will be the standard slab used on all girder superstructures except curved steel structures.

Concrete for prestressed panels shall be Class A1 with ${\displaystyle \,f'{c}}$ = 6,000 psi, ${\displaystyle \,f'_{ci}}$ = 3,500 psi. Prestressing tendons shall be uncoated, low-relaxation, seven-wire(7) strands for prestressed concrete conforming to AASHTO M203 Grade 270, with nominal diameter of strand = 3/8" and area = 0.085 sq.in., minimum ultimate strength = 22.95 kips (270 ksi), and strand spacing = 4.5 inches.

Panels shall be set on joint filler or polystyrene bedding material. Filler thickness shall be a Min. of 3/4" and a Max. of 2". Standard filler width is 1 1/2" except at splice plates where 3/4" Min. is allowed to clear splice bolts. Joint filler thickness may be reduced to a minimum of 1/4" over splice plates on steel structures. For prestressed girder structures, joint filler thickness may be varied within these limits to offset girder camber or at the contractor's option a uniform 3/4" (Min.) thickness may be used throughout. The same thickness shall be used under any one edge of any panel and the maximum change in thickness between adjacent panels shall be 1/4".

Standard roadway cross sections and slab reinforcement for HS20 and HS20 Modified live loads are shown in this section. Reinforcement shown is for a cast-in-place slab or a P/S panel slab with the bottom layer of reinforcement between girders being replaced by the panels. Cantilever reinforcement details for P/S panel slab are shown in this section.

Maximum panel width (clear span + 6") = 9'-6" for HS20 Modified.
Maximum panel width (clear span + 6") = 9'-11" for HS20.

When a barrier or railing is permanently required on the structure, other than at the edge of slab, precast prestressed panels will not be allowed in the bay underneath the barrier or railing. Prestressed panels are not allowed for use as simply supported for live loads, i.e. staging, where only two supports may be provided for live loads.

S.I.P.

Stay-in-place corrugated metal forms with cast-in-place concrete may be used on horizontally curved steel structures with the approval of the Structural Project Manager.

The standard slab reinforcements shown in this section for HS20 live load were designed using S.I.P. Dead Loads. If design is for HS20 Modified, the standard slab reinforcement needs to be checked for S.I.P. forms.

The bottom transverse reinforcement shall maintain a 1" clear distance from the top of forms.

C.I.P.

8 1/2" cast-in-place concrete slab with conventional forming may be used at the contractor's option, on all girder structures. Conventional forming shall also be used between girders with stage construction joints.

Section Thru Const. Joint Section A-A (1) End panels shall be dimensioned 1" min. to 1-1/2"max. from the inside face of diaphragm. (2) S-Bars shown are bottom steel in slab betweenpanels and used with squared end panels only. (3) Extend S-Bars 18 inches beyond the frontface of end bents only. (*) Adjust the permissible construction joint to a clearance of 6inches minimum from the joints of the panels. Note: All reinforcement other than prestressing strands shallbe epoxy coated. (**) 3/4" Min. thru 2" max. thickness and 1 1/2" width ofpreformed fiber expansion joint material or Sec 1057or polystyrene bedding material Sec 1073.

End Bent End Bent (Integral) Int. Bent (Exp. Gap) (1) End panels shall be dimensioned 1" min. to 1 1/2" max. from the inside face of diaphragm. (2) S-Bars shown are bottom steel in slab between panels and used with squared end panels only. (3) Extend S-bars 18 inches beyond the front face of end bents only. Section A-A(*) Over splice plates, 3/4" Min. thickness allowed. (5) S-Bars shown are used with skewed end panels, or square end panels of square structures only. The #5-S Bars will extend the width of slab (30" lap if necessary) or to within 3" of expansion device assemblies. Note: All reinforcement other than prestressing strands shall be epoxy coated. Part Section B-B Section Thru Cantilever

Plan of Precast Prestressed Panel Plan of Precast Prestressed Panel(Skewed End-Optional) (*) = 3" (Typ.) for steel girder structures (*) = 3" (Typ.) for P/S girder structures (**) Use #3-P3 bars if panel is skewed ${\displaystyle \,45^{\circ }}$ or greater. Note: Area of Strand = Astra = 0.085 sq. in./strandInitial prestressing stress = fsi = (0.75)(270 ksi) = 202.5 ksiInitial prestressing force = Astra x fsi= (0.085 sq. in./strand)(202.5 ksi) = 17.2 kips/strand

#### 751.40.8.5.2 Timber Floor

Maximum stringer spacing as determined by strength of timber floor
Stress = 1,200 lbs. per square inch
H-10 H-15
(*) 3" x 12" Plank 18" + 1/2 Flange Width 16" + 1/2 Flange Width
4" Laminated Floor 2'-11" + 1/2 Flange Width 2'-3" + 1/2 Flange Width
6" Laminated Floor 6'-0" + 1/2 Flange Width 4'-4" + 1/2 Flange Width
Stress = 1,600 lbs. per square inch
H-10 H-15
3" x 12" Plank 23" + 1/2 Flange Width 21" + 1/2 Flange Width
4" Laminated Floor 3'-9" + 1/2 Flange Width 2'-11 1/2" + 1/2 Flange Width
6" Laminated Floor 7'-10 3/4" + 1/2 Flange Width 5'-9" + 1/2 Flange Width
(*) 3" x 12" Plank without treads.

#### 751.40.8.5.3 Steel Grid Bridge Flooring

In general, the 5" depth (concrete filled to half depth) steel grid bridge flooring shall be specified. Bar spacing may vary as necessary to meet minimum section modulus requirements. Main member spacing shall not exceed 10" and cross bar spacing shall not exceed 4". At present, the manufacturers of the following types have provided data to show they are acceptable:

Greulich 5" Standard
Foster 5" Standard

The section properties ${\displaystyle \,(n=8)}$ and maximum span for HS20 loading have been computed for these types and are as follows:

 Company (For DesignPurpose only)Weight (PSF)(Steel & Conc.) Main barSpacing Cross barSpacing Moment of Inertia${\displaystyle \,(in^{4}/Ft.)}$ Mid Span Over-Support Conc. Steel Steel Greulich 48.0 7 1/2" 3 3/4" 99.41 12.43 9.03 Foster 48.0 8" 4" 128.1 16.01 12.25

 Company Section Modulus ${\displaystyle \,(in^{2}/ft.)}$ Maximum Span (*) Mid-Span Over-Support Simple Span Continuous Spans Conc.(Top) Steel(Bott.) Steel(Top) Steel(Bott.) ASTMA709Gr. 36 ASTMA709Gr. 50W ASTMA709Gr. 36 ASTMA709Gr. 50W Greulich 59.5 3.53 3.90 3.14 4'-4" 5'-10" 5'-10" 7'-1" Foster 72.5 4.68 5.25 4.30 5'-9" 7'-5" 7'-2" 9'-4"

The cross-section DETAILS used in computing the section properties are shown on the sketches on the following sheets. Maximum span determination included an allowance for a 35#/sq.ft. future wearing surface and assumed a wheel load to be distributed, normal to the main bars, over a width of 4'-0".

(Place the following note on the Bridge Plans with the Steel Grid Details.

Note: The steel grid deck shall be electrically grounded.

(*) For main beams of grid either parallel or perpendicular to traffic.

 Composite Section Steel Section Only (net) y 1.671" 2.317"

Greulich 5" Standard
 Note: Dimensions obtained form Greulich plans.

 Composite Section Steel Section Only (net) y 1.766" 2.338"

Foster 5" Standard
 Note: Dimensions obtained form Foster Catalog.

#### 751.40.8.5.4 Longitudinal Diagrams

##### 751.40.8.5.4.1 Hinged Beam Connections

The diagrams of various joints in steel structures are intended to be guides primarily for the determination of horizontal longitudinal dimensions for the plan view on the first sheet of plans.

These diagrams are not to be detailed on the design plans. However, the arrangement of the joints should be useful in detailing the longitudinal diagram for structural steel, particularly for bridges on grades and vertical curves.

Longitudinal dimensions for the plan of structural steel and for the plan of slab shall be horizontal from centerline bearing to centerline bearing.

For proper correlation of details when developing plans for widening or redecking bridges, match the method of dimensioning on the new plans with the method used on the originals.

##### 751.40.8.5.4.2 Longitudinal Sections
 (*) Parallel to Girder. All other dimensions shown are normal to backwall. (**) See EPG 751.13 Expansion Devices for dimension of overhang from end of stringer or girder to face of plate, edge of concrete or face of vertical leg of angle.

 (*) Parallel to Girder. All other dimensions shown are normal to backwall. (**) 18" min. (Use same dimension as the expansion device end on 3-span continuous, if it is not more than 2" greater.) (***) 3" min. for type C, D and E bearing, and 2" min. for an elastomeric bearing.

 1/2" minimum overhang from end of stringer to face of plate, edge of concrete or face of vertical leg of angle. Gap as required for a particular type of expansion device. Expansion device gap plus 1 1/2" minimum (taken parallel to centerline stringer). (*) Parallel to Girder. All other dimensions shown are normal to centerline Bent. Blockout shown is for Elastomeric Expansion Joint Seal. CheckBridge Memorandum for type of device for a particular structure.

 BLOCKING DIAGRAM SHOULD NOT BE USED FOR CAMBERED GIRDERS. Note: The typical elevation shown above should be detailed on the plans for all steel structures that are on vertical curve grades. (1) Longitudinal dimensions are horizontal from centerline Brg. to centerline Brg. (*) Horizontal dimensions.

#### 751.40.8.5.5 Miscellaneous Bearing Connections

##### 751.40.8.5.5.1 Typical Details of “Hinged Connection"
Section Showing Hinged Beam Connection

Plan of Brg. Plate
Detail of Web at
Typical Welding Details
for Stiff. Plates

 "D" Gap as required for expansion (3" Min.) "J" 5" for bearing with 3" web thickness. Use 6" for all others. Dimension to be 1/3 brg. length (Typ.) (*) To be used unless greater depth is required by design. (**) See EPG 751.13 Expansion Devices Note: Web thickness and size of fillet weld connecting bearing stiffener plate to web as required by design. Plans for bridges on a grade or vertical curve shall have the conn. detailed in relation to the slope of the girders and stringers.
Section C-C

 (*) See below for dimension "G". (**) See EPG 751.13 Expansion Devices "F" = Gap as required for expansion (3" Min.). "H" = 10 3/4" Min. (12" preferred.) "J" = 5" for bearing with 3" web thickness. Use 6" for all others. All dimensions shown are minimum, increase, as necessary.

WebThickness Depth"G" (*) AllowableDead LoadReactions, Kips(At 150% Overstress) WebThickness Depth"G" (*) AllowableDead LoadReactions, Kips(At 150% Overstress) 5/16" 8" 45.0 7/16" 8" 63.0 5/16" 9" 50.6 7/16" 9" 70.8 5/16" 10" 56.2 7/16" 10" 78.7 5/16" 11" 61.8 7/16" 11" 86.6 5/16" 12" 67.5 7/16" 12" 94.5 5/16" 13" 73.1 7/16" 13" 102.3 5/16" 14" 78.8 7/16" 14" 110.2 5/16" 15" 84.3 7/16" 15" 118.1

 3/8" 8" 54 1/2" 8" 72.0 3/8" 9" 60.7 1/2" 9" 81.0 3/8" 10" 67.5 1/2" 10" 90.0 3/8" 11" 74.2 1/2" 11" 99.0 3/8" 12" 81 1/2" 12" 108.0 3/8" 13" 87.7 1/2" 13" 117.0 3/8" 14" 94.5 1/2" 14" 126.0 3/8" 15" 101.2 1/2" 15" 135.0
(*) No (Live load + impact) excluded.

 Note: Modify standard end diaphragm connections as shown above, if clearance problems exist between bearing plate and end diaphragm connection bolts.

### 751.40.8.6 Composite Design

#### 751.40.8.6.1 General

GENERAL

This portion of the article pertains to structures composed of steel girders with concrete slab connected by shear connectors. The stresses of composite girders and slab shall be computed based on the composite cross-section properties and shall be consistent with the properties of the various materials used. The regions subjected to positive moment are considered as composite and the regions subjected to negative moment are considered as non-composite. For the initial girder design, composite/non-composite regions can be approximately assumed as:

SECTION PROPERTIES

Cross-section properties of the composite section shall include concrete slab and steel section.

Cross-section properties of the non-composite section shall include steel section only.

Use composite property for positive moment section.

Use non-composite property for negative moment section. The effect of reinforcing steel in the section is not considered.

The ratio of modulus of elasticity of steel to that of concrete, n, shall be assumed to be eight. The effect of creep shall be considered in the design of composite girders which have dead loads acting on the composite section. In such structures, n=24 shall be used.

DESIGN UNIT STRESSES (also see note A1.1 in EPG 751.50 Standard Detailing Notes)

Reinforcement Concrete

 Reinforcing Steel (Grade 60) ${\displaystyle \,f_{s}}$ = 24,000 psi ${\displaystyle \,f_{y}}$ = 60,000 psi Class B-2 Concrete (Substructure) ${\displaystyle \,f_{c}}$ = 1,600 psi ${\displaystyle \,f'_{c}}$ = 4,000 psi

Structural Steel

 Structural Carbon Steel (ASTM A709 Grade 36) ${\displaystyle \,f_{s}}$ = 20,000 psi ${\displaystyle \,f_{y}}$ = 36,000 psi Structural Steel (ASTM A709 Grade 50) ${\displaystyle \,f_{s}}$ = 27,000 psi ${\displaystyle \,f_{y}}$ = 50,000 psi Structural Steel (ASTM A709 Grade 50W) ${\displaystyle \,f_{s}}$ = 27,000 psi ${\displaystyle \,f_{y}}$ = 50,000 psi

#### 751.40.8.6.2 Design

##### 751.40.8.6.2.1 Shear Connector Design

The shear connectors shall be designed for fatigue and checked for ultimate strength (AASHTO Article 10.38.5.1).

Step 1:

Compute Vr, the range of shear in kips, from the structural analysis, due to live loads and impact, for entire span.

At any section, the range of shear shall be taken as the difference in the minimum and maximum shear envelopes (excluding dead loads).

Step 2:

Use the average Vr per span, for the section of the span that is assumed to act compositely (from end of span to point of contraflexure for end spans, or from point of contraflexure to point of contraflexure for int. spans).

Step 3:

Using the average Vr from step 2, compute the range of horizontal shear load per linear inch, Sr in kips per inch, at the junction of the slab and stringer from the following equation:

${\displaystyle \,\ Sr={\frac {VrQ}{I}}}$

(AASHTO Article 10.38.5.1.1 Eq. 10-58)

where:

${\displaystyle \,Q}$ = static moment of the transformed compressive concrete area about the neutral axis of the composite section, in cubic inches (*);

${\displaystyle \,I}$ = moment of inertia of the transformed composite girder in positive moment regions in inches to the fourth power (*).

(*) In the formula, the compressive concrete area is transformed into an equivalent area of steel by dividing the effective concrete flange width by the modular ratio n=8.

Step 4:

Compute the allowable range of horizontal shear, Zr, in pounds on an individual connector, welded stud, by use of the following formula:

${\displaystyle \,Zr=\alpha \ d^{2}}$

where:

${\displaystyle \,{\frac {H}{d}}\geq 4}$

${\displaystyle \,H}$ =height of stud in inches;

${\displaystyle \,d}$ =diameter of stud in inches;

${\displaystyle \,\alpha }$ =13,000 for 100,000 cycles

10,600 for 500,000 cycles
7,850 for 2,000,000 cycles
5,500 for over 2,000,000 cycles.

Step 5:

Compute the number of additional connectors required at point of contraflexure, N , from the following formula:

Pitch = ${\displaystyle \,{\frac {\sum Z_{r}}{S_{r}}}}$

Where: Pitch = required pitch, in inches;

${\displaystyle \,\sum Z_{r}}$ = the resistance of all connectors at one (1) transverse girder cross-section as a shear connector unit.

Note:

The pitch is to be constant and spaced in the composite section (round to the nearest inch).

Step 6:

Compute the required pitch of the shear connector units, pitch by the following formula:

${\displaystyle \,N_{c}={\frac {{A_{r}}^{2}f_{r}}{Z_{r}}}}$

(AASHTO Article 10.38.5.1.1 Eq. 10-69)

where:

${\displaystyle \,N_{c}}$ = number of additional connectors required at the point of contraflexure;

${\displaystyle \,{A_{r}}^{s}}$ = total area of longitudinal slab reinforcing steel for each girder over interior support;

${\displaystyle \,f_{r}}$ = range of stress due to live load plus impact, in the slab reinforcement over the support (in lieu of more accurate computations, f may be taken as equal to 10,000 psi);

${\displaystyle \,Z_{r}}$ = the allowable range of horizontal shear on an individual connector.

This number of additional connectors, N , shall be placed adjacent to the point of dead load contraflexure within a distance equal to 1/3 of the effective slab width, if it is possible. If it is impossible, use minimum pitch of 6".

Step 7: Check connectors for ultimate strength

The number of connectors provided for fatigue must be checked to ensure that adequate connectors are provided for ultimate strength.

To check for ultimate strength, proceed as follows:

(1) Compute the force in the slab (P), which is defined as: at the point of maximum positive moment, the force in the slab is taken as the smaller value of the following two formulae:

${\displaystyle \,P_{1}=A_{s}F_{y}}$ (AASHTO Article 10.38.5.1.2 Eq. 10-63)

or

${\displaystyle \,P_{2}=0.85f'_{cbt_{s}}P}$ = (AASHTO Article 10.38.5.1.2 Eq. 10-62)

Where:

${\displaystyle \,A_{s}}$ = total area of the steel section including cover plates (if used);

${\displaystyle \,F_{y}}$ = specified minimum yield point of the steel being used;

${\displaystyle \,f'_{c}}$ = compressive strength of concrete at age of 28 days;

${\displaystyle \,b}$ = effective flange width given in AASHTO Article 10.38.3;

${\displaystyle \,t_{s}}$ = thickness of concrete slab.

Note:

If it becomes impractical to place the number of shear connectors required by ultimate strength in the specified distance (structures with span ratios greater than 1.5); base the number and spacing of shear connectors on the fatigue analysis only.

Increase the haunch by 1/2"± more than what is required to make one size shear connector work for C.I.P. or S.I.P. option.

##### 751.40.8.6.2.2 Shear Connector Spacing

If it becomes impractical to place the number of shear connectors required by ultimate strength in the specified distance (structures with span ratios greater than 1.5); base the number and spacing of shear connectors on the fatigue analysis only.

For a typical 3-spans bridge, the shear connector units can be approximately arranged as below:

#### 751.40.8.6.3 Details

##### 751.40.8.6.3.1 Shear Connector Details

Use precast prestressed panels on all tangent steel structures. Evaluate the viability of the use of P/S panels on curved structures on a case by case basis and use or include as an option to a CIP slab where deemed appropriate.

Whenever panels are used, the minimum top flange width shall be 12" for Plate Girders and 10" for Wide Flange Beams.

Steel girders shall be cambered when using P/S Panels. Minimum joint filler thickness is 3/4", except over splice plates, in which case use 1/4" minimum. Maximum joint filler thickness is 2".

Shear connectors shall have a minimum height equal to the top of panel.

Shear connectors shall be spaced by units and shear connectors in each unit shall be placed along ${\displaystyle \,C_{\!\!\!\!L}}$ of girder. On wide flange widths, two lines of connectors may be used if spacings and clearances allow.

Additional shear connectors, Nc, at point of contraflexure may be placed in units normal to ${\displaystyle \,C_{\!\!\!\!L}}$ girder as space allows or in a single row along ${\displaystyle \,C_{\!\!\!\!L}}$ girder as shown below:

P/S strands shall extend 3" minimum and 6" maximum past edge of precast prestressed panel and not closer than 1" to the adjacent panels.

Panel end at splices shall be notched to avoid bolt heads as shown below:

3/4" min. wide bearing edge for panel at splice, typ. (*)

1-1/4" min. (Typ.)

4 x (Stud diameter) preferred minimum, may be reduced if necessary for a more economical design; 2-1/4" absolute minimum.

(*) In order to meet and above, it is necessary to have an edge bolt distance of 2" or greater for splice plate. For unusual cases, which would require field splices for flange widths 14" or 15" for P/S precast panel option, it will be necessary to change the top flange width to either 13" or 16" of equal area to maintain the 3/4" minimum panel bearing edge on the splice plates.

Minimum joint filler thickness is 3/4" except over splice plates in which case use 1/4" minimum. When joint filler is less than 1/2" thick over splice plate, make the width of joint filler at splice the same width as panel on splice (maximum 1-1/2" wide).

Maximum difference in top of flange thickness should be checked so that joint filler thickness does not exceed 2".

##### 751.40.8.6.3.2 Deflection

 1 Composite Design: Defl. = 1/1000 of span; 2 Non-composite Design: Defl. = 1/800 of span

Where:
Defl. = allowable deflection due to service live load plus impact.

Dead Load Deflection Compute at 1/4 point for bridge with spans less than 75’, at 1/10 points for spans 75’ and over.

### 751.40.8.7 Wide Flange Beam Spans

#### 751.40.8.7.1 Design

##### 751.40.8.7.1.1 Design Data

Slabs

 Reinforcing Steel ${\displaystyle \,f_{y}}$ = 60,000 psi Concrete ${\displaystyle \,f_{c}}$ = 1,600 psi ${\displaystyle \,f'_{c}}$ = 4,000 psi ${\displaystyle \,n}$ = 8

Simple Design Span

Design Span = Center to Center of Bearings.

 Composite ${\displaystyle \,{\frac {L}{1000}}}$ Non-Composite ${\displaystyle \,{\frac {L}{800}}}$

Live Load ${\displaystyle \,(LL)/}$ Wheel Line ${\displaystyle \,(WL)}$ is the Live Load Reaction per Wheel Line, no distribution, no impact; Maximim Live Load ${\displaystyle \,(LL)+}$ Impact ${\displaystyle \,(I)}$ is the Live Load Reaction x Distribution Factor = Impact.

(Governs thru 33' simple spans for H20 and all simple spans for HS20)

(Governs for simple soabs 35' and over for H20)

Typical Continuous Steel Structures - Integral End Bents:

(*) Maximum length for End Bent to end Bent - 500 feet.
##### 751.40.8.7.1.2 Stringer Design

Stresses:

 Steel: AASHTO - Article 10.2, 10.32 ASTM A709 Grade 36 ${\displaystyle \,f_{y}}$ = 36,000 psi ( ${\displaystyle \,f_{s}}$ = 20,000 psi) ASTM A709 Grade 50 & Grade 50W ${\displaystyle \,f_{y}}$ = 50,000 psi ( ${\displaystyle \,f_{s}}$ = 27,000 psi)

 Superstructure Concrete: ${\displaystyle \,f_{c}}$ = 1,600 psi ${\displaystyle \,f'_{c}}$ = 4,000 psi ${\displaystyle \,n}$ = 8

 Reinforcing Steel: ${\displaystyle \,f_{y}}$ = 60,000 psi

Physical Properties of Spans

Composite Design - See Widening and Repair - Composite Design.
Non-Composite Design - Use "Constant I" analysis.

When the neutral axis of a composite section falls in the concrete fange, the section shall be designed as Non-Composite (21" Wide Flange is the smallest beam generaly made conposite).

Deflection

 Live Load Deflection: AASHTO - Article 10.6 Composite - Allowable Deflection L/1000 Non-Composite - Allowable Deflection l/800 Dead Load Deflection: Compute at 1/4 points for bridges with spans less than 75', at 1/10 points for spans 75' and over. Give percentage of deflection due to weight of structural steel.

Fatigue Stress

AASHTO - Article 10.3 Case I, Case II or Case III (as specified on Bridge Memorandum generally within the following limitations).

 Case I: Bridges with the TRUCK traffic count of 2500 or more vehicles per day (one direction). Case II: Bridges with traffic count of 750 or more vehicles per day, and less than 2500 TRUCK traffic count (one direction) per day. Case III: Bridges with traffic count of less than 750 vehicles per day, except when Live Loading is H20 or greater. No Fatigue: Bridges with traffic of less than 75 vehicles per day.

Economic Comparison

When comparing cost of low-alloy steels (A-572, Gr.-50, and A-588) to the cost of A-36 steel, the low-alloy steels shall be figured a t 3 1/2 cents for A-572, Gr.-50 and 5 1/4 cents for A-588 per pound more than A-36 steel. Cost comparisions will be based on current average bid prices that may be obtained from the CHIEF DESIGNER, for comparable bridges.

No overstressed will be permitted in the design.

In no case shall an exterior stringer have less carrying capacity than an interior stringer.

##### 751.40.8.7.1.3 Flange Plate Lengths

Allowable flange plate sizes are as shown with the section properties. Different plate sizes may be used on adjacent stringers.

Lengths to be shown on the bridge plans are those required as follows:

Lengths each side of the bearing shall be the larger of:
1. Theoretical End + Terminal Distance (***) or
2. Point where the stress range (tension or reversal) in the beam flange is equal to or less than allowable fatigue stess range (Cat. E or E') or where the beam flange is in compression, whichever is smaller.
• Use Cat. E when the flange is less than or equal to 0.8 inch thick.
• Use Cat. E' when the flange is greater than 0.8 inch thick.

(***) Where the theoretical end = the point where the flange stress without cover plate less than or equal to base allowable stress. Terminal distance = 1 1/2 times nominal cover plate width.

The total length of the cover plate greater than or equal to (2D + 3'-0"). Where "D" = Depth of beam in feet.

When required lengths of plates vary by 12" or less on adjacent stringers or on each side of the centerline stiffener plate, use greater length for all such positions.

Plate lengths taken form the computer programs should be rouned up to at least the nearest 6".

### 751.40.8.8 Welded Plate Girders

#### 751.40.8.8.1 Design

##### 751.40.8.8.1.1 Design Assumptions & Procedures

Design Unit Stresses

 Reinforcement Concrete Reinforcing Steel (Grade 60) ${\displaystyle \,f_{s}}$ = 24,000 psi, ${\displaystyle \,f_{y}}$ = 60,000 psi Class B2 Concrete (Superstructure) ${\displaystyle \,f_{c}}$ = 1,600 psi, ${\displaystyle \,f'_{c}}$ = 4,000 psi

 Structural Steel: Structural Carbon Steel (ASTM A709 Grade 36) ${\displaystyle \,f_{s}}$ = 20,000 psi, ${\displaystyle \,f_{y}}$ = 36,000 psi Structural Steel (ASTM A709 Grade 50) ${\displaystyle \,f_{s}}$ = 27,000 psi, ${\displaystyle \,f_{y}}$ = 50,000 psi Structural Steel (ASTM A709 Grade 50W) ${\displaystyle \,f_{s}}$ = 27,000 psi, ${\displaystyle \,f_{y}}$ = 50,000 psi

Design Procedure:

Moments and shears by "Variable I" analysis:

use computer program.

Trial sections from "Preliminary analysis":

Combination of web depth, flanges and length of plates used shall be the most economical section available with depths compatible with vertical clearance requirements. Web depths in 6" increments are preferred, however other increments may be used when required by the Bridge Memorandum. (See Structural Project Manager)

Flanges:

Minimum flange dimensions = 3/4" x 12" (*).

Increments:

Thickness 1/8"
Width 1"

Maximum flange dimensions:

Reference AASHTO - Table 10.32.1A)
maximum thickness = 4"

Note: It is preferred office practice to maintain the same flange thickness at as many locations as practical. This can be accomplished by varying the flange width.

(*) For shipping and erection purposes, minimum width of both compression and tension flanges shall not be less than L/85 where L is the shipping length of the girder. This limitation is for preventing out-of-plane distortion of the girder.

Webs:

Web dimensions:

(Reference AASHTO - Article 10.34 & 10.48)
ASTM A709 Grade 36 = 3/8" minimum thickness for curved girders and for continuous straight girders.
ASTM A709 Grade 50W = 3/8" minimum thickness.
AASHTO - Article 10.3 Case I, Case II or Case III.
Case I
Bridges with the truck traffic count of 2500 or more vehicles per day. (One direction)
Case II
Bridges with traffic count of 750 or more vehicles per day, and less than 2500 truck traffic count (One direction) per day.
Case III
Bridges with traffic count of less than 750 vehicles per day, except when live loading is H20 or greater.
No Fatigue:
Bridges with traffic count of less than 75 vehicles per day.

Total Capacity of Exterior Girders:

In no case shall an exterior girder have less carrying capacity than an interior girder.

Horizontal Curved Girders Design Procedures (*)

Curved plate girders are to be designed using load factor design criteria. The 1980 AASHTO Guide Specifications for Horizontally Curved Highway Bridges as revised by Interim Specifications for Bridges 1981, 1982, 1984, 1985 and 1986 is to be applied with the USS Highway Structure Design Handbook (\) V-Load method to be used as a working example.

The following procedure may be followed to determine the required cross-section for any system of curved girders with skews less than 46°.

1. Determine the primary moments by the same procedures as for a system of straight girders, using the developed lengths of the curved girders.

2. From primary moments, compute shear loads, ${\displaystyle \,V}$, using the formula:

 ${\displaystyle \,V={\frac {\sum M}{Coeff.*K}}}$ ${\displaystyle \,V}$ = Shear loads.M = Primary moments. ${\displaystyle \,K={\frac {RD}{d}}}$ ${\displaystyle \,R}$ = Radius of curvature (outside girder).${\displaystyle \,D}$ = Radial distance between inside and outside girders.${\displaystyle \,d}$ = Distance between diaphragms measured along axis of outside girder.

The following coefficients may be applied to "${\displaystyle \,K}$" for the various multiple-girder systems with equal spacing between girders.

 SYSTEM COEFFICIENTFRACTION COEFFICIENTDECIMAL 2 girders 1 1.00 3 girders 1 1.00 4 girders 10/9 1.11 5 girders 5/4 1.25 6 girders 7/5 1.40 7 girders 14/9 1.56 8 girders 12/7 1.72 9 girders 15/8 1.88 10 girders 165/81 2.04

3. Compute ${\displaystyle \,V-Load}$ moments

• Reference: USS "Highway Structures Design Handbook" 1965 Edition. (Updated 1986 Volume II Section 6) developed by Richardson, Gordon and Associates in cooperation with Dr. John Scalzi is to be used as a working example.

4. Compute lateral bending moments using the approximate formula:

 ${\displaystyle \,M_{L}={\frac {Hd}{10}}={\frac {Md^{2}}{10Rh}}}$ ${\displaystyle \,ML}$ = Lateral bending moment ${\displaystyle \,H}$ = The ${\displaystyle \,H}$ values are approximately equal to the reactions at the supports. ${\displaystyle \,h}$ = Depth of girder between centers of gravity of flanges. ${\displaystyle \,M}$ = Primary moment + Secondary moment.

5. Determine cross-section required to provide for vertical and lateral forces computed under Items 1 to 4 inclusive. As with any statically indeterminate system it is necessary to make an initial assumption of the required cross-sections and to repeat the calculations one or more times to obtain reasonable agreement between the assumed and required sections.

6. The non-compact section requirement that ${\displaystyle \,F_{y}>(f_{b}+f_{w})}$ is to be applied to all sections with the tension flange ${\displaystyle \,F_{y}>(f_{b}+f_{w})}$ and the compression flange as ${\displaystyle \,F_{y}(1-3\lambda ^{2})>(f_{b}+f_{w})}$ to ensure conservative design.

In computing ${\displaystyle \,\lambda }$, use ${\displaystyle \ell }$ to be actual diaphragm spacing for compression and tension stresses.

The value of ${\displaystyle \,f_{w}}$ is to be selected as plus or minus in the equations for ${\displaystyle \,P_{w}}$ to give the worst possible case.

Design and Detail Guides

1. Economic Arrangement of Spans and Depth-to-Spans Ratios

Where there is flexibility in span arrangement, the same guides that apply to economic arrangement of straight girders are equally applicable to curved girders. Similarly the rules used to establish depth-to-span ratios for straight girders usually will apply to curved girders.

2. Spacing of Girders

Spacing depends on the arrangements of diaphragms and bracing. In general, however, it will be found that the most economical arrangement for straight girders will accord very well with the best arrangement for a system of curved girders. The effect of curvature increases in proportion to the square of the span length and decreases in proportion to the radius of curvature and the spacing of girders.

3. Arrangement and Spacing of Diaphragms

The diaphragms shall be placed radially, with a maximum spacing of 15'-0". In order to minimize lateral bending of the girder flanges, the flanges should be as wide as practical.

Sway frame bracing is selected for curved girder system, by same methods as for straight girders.

4. Effect of Lateral Bracing

made in a similar manner as for straight bridges. If lateral Provision for lateral loading on curved girders may be bracing is used in a system of curved girders, the forces resulting from the radial components of flange stress may be carried partially or entirely by the bracing system; when both diaphragms and lateral bracing are used, radial reaction components may be divided between the two systems.

5. Approximate Estimate of Curvature

The following formula may be used in making preliminary approximations of the effect of curvature:

 ${\displaystyle \,P=10.5\times {\frac {(1+r)(L')^{2}}{R_{2}D}}}$ Note: For "r" refer to paragraph No. 7 ${\displaystyle \,r={\frac {(R_{1})^{2}}{(R_{2})^{2}}}\times {\bigg (}{\frac {Inside\ girder\ loading)}{Outside\ girder\ loading}}{\bigg )}}$ (*)

 (*) May be omiteed if supports are on radial lines. ${\displaystyle \,P}$ % increase in positive moment due to effect of curvature. ${\displaystyle \,R_{2}}$ Radius of inside girder. ${\displaystyle \,R_{1}}$ Radius of outside girder. ${\displaystyle \,L'}$ Distance between points of contraflexure in any pisitive moment area. ${\displaystyle \,D}$ Spacing between inside and outside girders.

In the above form, the formula applies to a two-girder system, but it may be modified by reference to the table of coefficients for multiple-girder systems shown in Item #2. From primary moments, compute shear loads.

The formula applies particularly to positive moment, but for preliminary approximation it may be assumed that the curvature effect on negative moments will be about the same.

6. Design of Diaphragms and Connections

Where the degree of curvature is equal to or under 1° - 30' and when spans are equal to or under 75'-0" in length, the diaphragm and connections shall be the same as for Bridges with straight girders. Where the degree of curvature is over 1°- 30' to 3° or with a span length of more than 75'-0", the diaphragm must be attached to the tension flange. Where the degree of curvature is over 3°, a special design will be required for connection of intermediate diaphragms to flanges.

The maximum allowable diaphragm spacing is 15'-0", regardless of the amount of curvature, or span lengths.

The following applies to those bridges where the special design is to be considered:

Since diaphragm moments due to effect of curvature are a function of the radial component of flange stress, they are directly proportional to the vertical bending moment in the girders.

For exterior girders the moment in the diaphragm equals ${\displaystyle \,M\times d/R}$, in which ${\displaystyle \,M}$ = vertical bending moment in girder for any particular condition of loading; ${\displaystyle \,d}$ = diaphragm spacing; ${\displaystyle \,R}$ = Radius of curvature of girder.

For negative moment over the support, the ${\displaystyle \,M}$ value used in this equation should be the average moment between a point at the support and a point at the first adjacent diaphragm.

Diaphragm connections may be made directly to the flanges of the girders or through stiffeners, provided details are arranged to adequately transfer radial components of flange stress into the diaphragms.

7. Supports positioned other than on radial lines.

If field conditions permit, the most orderly arrangement for curved girders will be attained by placing the supports on radial lines.

It may be necessary to treat each line of girders independently, first finding the direct loading moments and then correcting for curvature by applying the separate ${\displaystyle \,V-loads}$.

8. Transverse stiffeners

The maximum transverse stiffener spacing for curved plate girders is ${\displaystyle \,D}$, the web height.

Transverse stiffeners should be placed along the girder length only as far as required by design.

The maximum spacing of the first transverse stiffener at the simple support end of a curved plate girder is ${\displaystyle \,D/2}$.

Reference:

AASHTO - Article 10.5
Limit radius of heat curved girders according to AASHTO Article 10.15.

Where the distance between field splices of curved girders exceeds that given by the following formula, a special note shall be placed on the plans.

 ${\displaystyle \,L}$ = ${\displaystyle \,{\sqrt {\frac {0.667\ x\ f_{s}\ x\ SM}{W}}}}$ (*) ${\displaystyle \,L}$ = Allowable distance between field splices, in feet. ${\displaystyle \,f_{s}}$ = Allowable fs of flange steel, in psi. e.g. use 20,000 psi for Grade 36 steel. ${\displaystyle \,W}$ = Weight of girder (flanges and web), in pounds per foot. ${\displaystyle \,SM}$ = Section Modulus of girder about x-x axis as shown, in inches cubed.

Note:

If flanges are of different sizes, use smaller Section Modulus.

See Structural Project Manager for allowable overstress.

(*) Derivation

Positive moment at centerline, ${\displaystyle \,Mom.={\frac {WL^{2}}{8}}\times 12}$
${\displaystyle \,fs={\frac {Mom.}{SM}}}$
Substitute mom. in fs equation.
${\displaystyle \,fs={\frac {WL^{2}\times 12}{8\times SM}}}$
solve for L
${\displaystyle \,L={\sqrt {\frac {8f_{s}\times SM}{12W}}}}$

Design Example

 Shape ${\displaystyle \,I_{xx}}$ PL 13" x 3/4" ${\displaystyle \,{\frac {0.75\times (13)^{3}}{12}}=137.31}$ PL 70" x 3/8" ${\displaystyle \,{\frac {70\times (0.375)^{3}}{12}}=0.31}$ PL 12" x 3/4" ${\displaystyle \,{\frac {0.75\times (12)^{3}}{12}}=108.00}$ ${\displaystyle Total\ I_{xx}}$ ${\displaystyle =245.62\ In.^{4}}$
SECTION A-A ${\displaystyle \,SM_{A}=I/C=245.62/6.5=37.79In.^{3}}$
${\displaystyle \,SM_{B}=I/C=245.62/6=40.94In.^{3}}$
 Weight per Foot of Girder PL 12" x 3/4" = 30.6 lbs./ft. PL 70" x 3/8" = 89.3 lbs./ft. PL 13" x 3/4" = 33.2 lbs./ft. Total = 153.1 lbs./ft.

From Formula:   ${\displaystyle \,L={\sqrt {\frac {0.667\times fs\times SM}{W}}}={\sqrt {\frac {0.667\times 20,000\times 37.79}{153.1}}}=57.38'}$ (Use 57.5')

57'-6" < 60'-0". Therefore, Special Note required.

Special Note:

Heat curving of girders (Identify) (*) will not be allowed shile in the horizontal position.

(*)Complete underlined portion as required.

Maximum Plate Lengths:

80 feet. See Structural Project Manager for use of longer lengths up to 85' for ASTM A709 Grade 50 or ASTM A709 Grade 50W and 100' for ASTM A709 Grade 36.

Minimum Plate Lengths:

10 feet. Shop flange splices should be eliminated and extra plate material used when :economy indicates and span lengths permit.

Preliminary Analysis:

(1) Compute moments from influence lines on basis of "Constant I" analysis and apply the following percentage increase or decrease to non-composite dead load moments.

References may be used in lieu of the above.

${\displaystyle \,n}$ = 1.2 to 1.5 ${\displaystyle \,n}$ = 1.2 to 1.5
 ${\displaystyle \,+M_{1}}$ -5% ${\displaystyle \,-M_{2}}$ +15% ${\displaystyle \,+M_{3}}$ -15%
 ${\displaystyle \,+M_{1}}$ -5% ${\displaystyle \,-M_{2}}$ +15% ${\displaystyle \,+M_{3}}$ -15% ${\displaystyle \,-M_{4}}$ +15%

(2) Determine trial sections and plot a rough moment curve to determine location of flange plate cutoffs, if any.

(3) Complete analysis by using computer programs to obtain actual moments and stresses.

Design Stress investigation for Positive Moment Area of Plate Girder Structure

The design stresses are to be checked at the top of flange (steel) and the top of concrete slab in the composible area of Plate Girder Structures to insure that they are within the allowable stresses.

SECTION A-A

Structure Length

Typical Continuous Steel Structures- Integral End Bents:

Estimated Girder Depth Based on Three Spans With Ratio N = 1.3±

 Initial Estimate(Feet) Girder Depths (*)(Inches) Structure Depth (**)(Feet) 85 to 104 42 4.50 105 to 124 48 5.00 125 to 134 54 5.50 135 to 144 60 6.00 145 to 159 66 6.50 160 to 174 72 7.00 175 to 184 78 7.50 185 to 194 84 8.00 195 to 204 90 8.50

Trial steel plate girder depths use program BR109 to check designs and deflections. Web depths may be adjusted by two inch increments.

(*) Bethlehem steel economic study (N = 1.3±). Bethlehem steel provided an economic study of multiple steel girder depths. The study indicated that cheaper designs are obtained by reducing the plate girder depths and reducing the number of stiffeners. The recommended initial estimates above are based on these designs.

(**) Structure depth includes slab and haunch.

A general rule of thumb is to determine the minimum web thickness without stiffeners; then, use a web thickness of one-sixteenth inch less. Match MoDOT requirements for web increments of one-sixteenth inch only.

If two-span structures are used, a deeper web is required. A good estimate is to use six inches additional depth than the above tables for two-span structures.

#### 751.40.8.8.2 Details

##### 751.40.8.8.2.1 Field Flange Splice – Bolted

General

Splices shall be designed using the Service Load Design Method and in accordance with AASHTO Articles 10.18,10.24 and 10.32 except as noted.

Splices shall be designed to develop 100% of the flange strength by the flange splice plate strength. When the flange section or steel grade changes at a splice, the smaller flange strength shall be used to design the splice. Splice plates shall then match the lower grade used in the flanges.

Minimum Yield Strength ${\displaystyle \,(Fy)}$ and Minimum Tensile Strength ${\displaystyle \,(Fu)}$

 ASTM A709 Grade 36 ${\displaystyle \,F_{y}}$ = 36 ksi ${\displaystyle \,F_{u}}$ = 58 ksi ASTM A709 Grade 50 ${\displaystyle \,F_{y}}$ = 50 ksi ${\displaystyle \,F_{u}}$ = 65 ksi ASTM A709 Grade 50W ${\displaystyle \,F_{y}}$ = 50 ksi ${\displaystyle \,F_{u}}$ = 70 ksi

Allowable Steel Stresses ${\displaystyle \,(F_{t})}$

Allowable stresses are determined by AASHTO Table 10.32.1A.

 Allowable tensile stress ${\displaystyle \,F_{t}=0.55\times F_{y}}$

 ASTM A709 Grade 36 ${\displaystyle \,F_{t}}$ = 20 ksi ASTM A709 Grade 50 ${\displaystyle \,F_{t}}$ = 27 ksi ASTM A709 Grade 50W ${\displaystyle \,F_{t}}$ = 27 ksi

Allowable Bolt Stresses

Splices shall be designed as slip critical connections with Class B surface preparation and oversized holes. Although standard holes are used in the fabrication of flange splices, designing the splices for oversize holes allows for some fabrication and erection tolerances. All splice bolts shall be 7/8" diameter ASTM A325 high strength bolts.

AASHTO Table 10.32.3C specifies ${\displaystyle \,F_{s}}$ = 19 ksi for a class B slip-critical connection. Tables shown in this article are based on 19 ksi that should also be used to design splices not listed in the table.

Although slip-critical connections are theoretically not subject to shear and bearing, they must be capable of resisting these stresses in the event of an overload that causes slip to occur. The allowable shear stress per bolt ${\displaystyle \,(Fv)}$ for bearing is 19 ksi with the threads included and ${\displaystyle \,1.25\times 19=23.75}$ ksi for threads not included.

Flange Strength

The flange strength shall be determined by multiplying the allowable stress of the flange by the area of the flange. The area of the flange shall be taken as the gross area of the flange, except that if more than 15 percent of each flange area is removed, that amount removed in excess of 15 percent shall be deducted from the gross area. Bolt holes are considered to be 1" diameter for the purpose of determining flange area.

Splice Plate Strength

The splice plate strength shall be determined by multiplying the allowable stress of the splice plates by the area of the splice plates. The area of the splice plates shall be taken as the gross area of the splice plates, except that if more than 15 percent of the splice plate area is removed, that amount in excess of 15 percent shall be deducted from the gross area.

Two Row Splices

Splices with two rows of bolts are used with flanges 12 to 13 inches wide. The inner and outer plates may either be the same length or the inner plate may be shorter. This is the case if the end bolts in the splice are only needed to be in single shear. All other bolts will be in double shear. (See Figure 3.42.2.2-1)

Figure 3.42.2.2-1

Four Row Splices

When the width of the flange being spliced is 14 inches or greater, four longitudinal rows of bolts are used. Three variations of the end bolts positioning may be used. In each of these variations, the last two bolts shall be located in the outer rows closest to the edge of the splice plate.

Figure 3.42.2.2-2

Flange Width Transitions

When the width of the flanges being spliced differs by more than 2", the larger flange shall be beveled as shown in Figure 3.42.2.2-3

Figure 3.42.2.2-3

Weight of Splice

When calculating the weight of splice, the following simplified weights shall be used.

Weight of High-Strength bolts (diameter 7/8") = 0.95 lbs/bolt

Unit weight of Structural Steel = 490 lbs/ft3

##### 751.40.8.8.2.2 Field Web Splice – Bolted

General

Splices shall be designed using the Service Load Design Method and in accordance with AASHTO Articles 10.18,10.24 and 10.32 except as noted.

The web splice consists of 2-Plates:

Thickness = 5/16" minimum.
Width = 12-1/2" (18-1/2" if 3 rows of bolts are required).

When the web section or steel grade changes at a splice, the smaller web strength should be used to design the splice.

Minimum Yield Strength ${\displaystyle \,(F_{y})}$ and Minimum Tensile Strength ${\displaystyle \,(F_{u})}$

 ASTM A709 Grade 36 ${\displaystyle \,F_{y}}$ = 36 ksi ${\displaystyle \,F_{u}}$ = 58 ksi ASTM A709 Grade 50 ${\displaystyle \,F_{y}}$ = 50 ksi ${\displaystyle \,F_{u}}$ = 65 ksi ASTM A709 Grade 50W ${\displaystyle \,F_{y}}$ = 50 ksi ${\displaystyle \,F_{u}}$ = 70 ksi

Allowable Steel Stresses ${\displaystyle \,(F_{b},F_{w})}$

Allowable stresses are determined by AASHTO Table 10.32.1A.

 Allowable bending stress ${\displaystyle \,F_{b}=0.55\times F_{y}}$ Allowable shear stress ${\displaystyle \,F_{v}=0.33\times F_{y}}$

 ASTM A709 Grade 36 ${\displaystyle \,F_{b}}$ = 20 ksi ${\displaystyle \,F_{v}}$ = 12 ksi ASTM A709 Grade 50 ${\displaystyle \,F_{b}}$ = 27 ksi ${\displaystyle \,F_{v}}$ = 17 ksi ASTM A709 Grade 50W ${\displaystyle \,F_{b}}$ = 27 ksi ${\displaystyle \,F_{v}}$ = 17 ksi

Allowable Bolt Stresses

Although standard holes are used in the fabrication of web splices, designing the splices for oversize holes allows for some fabrication and erection tolerances. Web splices required to resist shear between their connected parts are designated as slip-critical connections. Shear connections subjected to stress reversal, or where slippage would be undesirable, shall be slip-critical connections. Potential slip of joints should be investigated at intermediate load stages especially those joints located in composite regions. The resultant force shall be less than the allowable bolt shear force. All splice bolts shall be A325 7/8" diameter High Strength Bolts.

${\displaystyle \,F_{v}}$ = 19 ksi

Bolt Arrangement

The minimum distance from the center of any fastener in a standard hole to a sheared or thermally cut edge shall be 1-1/2 inches for 7/8" diameter fasteners. The minimum distance between centers of fasteners in standard holes shall be three times the diameter of the fastener, but shall not be less than 3 inches for 7/8" diameter fasteners.

Splice Plate Strength

The strength of the splice plates shall be determined by multiplying the allowable stress of the splice plates by the net area of all splice plates. The splice plates net area shall be taken as the gross area of the splice plates minus the bolt holes. Bolt holes are considered to be 1 inch diameter for the purpose of determining splice plate net area. Web splices are designed to develop 75% of net section of the web.

Web Strength

The strength of the web should be determined from the allowable web stress at the "top of web" to account for hybrid sections. Otherwise, the allowable web stress is based on a linear distribution of stress from outside face of flange to "top of web".

Weight of Splice

When calculating the weight of splice, the following simplified weights shall be used.

Weight of High-Strength bolts (diameter 7/8") = 0.95 lbs/bolt

Unit weight of Structural Steel = 490 lbs/ft3

### 751.40.8.9 Continuous Concrete Slab Bridges

#### 751.40.8.9.1 Slabs

##### 751.40.8.9.1.1 Design Assumptions
 Stresses - FC = 1600 psi N = 8 (Slab, Integral Column) FC = 1200 psi N = 10 (Open Bent, Footing) FY = 60,000 psi reinforcing steel

Use "Variable I" analysis for all structures except solid slabs without drop panels.
Use "Constant I" analysis for solid slabs without drop panels.

 "L" = Design Span "H" = Design Height "I" = Gross moment of inertia of the full cross-section (Slab minus voids - integral wearing surface not included) ("I1", "IA", etc. suggested I's to be considered.) "S" = The effective span length for the use in determining minimum slab thickness under load factor design (AASHTO 8.9).

Use the same column diameter and spacing for all Intermediate Bents.
Use the same slab thickness for all spans.

 DEGREE OF RESTRAINT - LONGITUDINAL Column Type Footing Type Top Column Bottom Column INT. BENTS Integral Column Spread or Pile Integral (**) Integral Column Pedestal Pile Integral (**) END BENTS Pinned Column any Pinned (**) Integral Pile (*) Pinned Open Bent with Column any Simple INT. BENTS Open Bent with Pile Simple

 (*) See EPG 751.40.8.9.2.5 Design Assumptions for Integral Piles. (**) Use "Pinned" for Seismic Performance Category A and "Fixed for Seismic Performance Categories B, C & D. (See Structural Project Manager or Liaison)
##### 751.40.8.9.1.2 Slab Design and Drop Panel

The Slab Depth is based on the following limitations:

 1. Vertical Clearance Requirements: see the Bridge Memorandum. 2. Allowable Depths: A. Positive Moments - see table of "Available Slab Depths and Void Data", in EPG 751.40.8.9.1.4 Slab Cross Section and Section Properties. B. Slab Depth controlled by the minimum thickness formula - (Integral wearing surface is included with the total depth provided.) Continuous Spans - AASHTO 8.9 = (S + 10)/30 "S" may be used as the clear distance between drop panels. Bridges may have two adjacent spans averaged if S2/S1 < 1.5 Simple Spans - AASHTO 8.9 = 1.2 (S + 10)/30 C. Negative Moments -

 DROP PANEL DEPTHS MIN. MAX. Bents in median of dual roadway 0" or 3" 13" Other Bents 0" or 3" 9" INCREMENTS OF 1"

 APPROXIMATE DROP PANEL WIDTH (FEET)(PARALLEL TO THE CENTERLINE OF ROADWAY) Bents Drop Panel Depth 4" 6" 7" 8" 9" 12" 3 Span Bridge 2 & 3 6' 6' 10' 8' 6' 4 Span Bridge 2 & 4 6' 6' 10' 8' 6' 3 8' 10' 12' 12' 12' 12' THESE WIDTHS ARE SUGGESTED ONLY AS TRIAL DIMENSIONS FORDESIGN AND ARE NOT TO BE USED AS LIMITS FOR THE FINAL DESIGN.

 3. Reinforcing Steel: A. Positive Moments = Maximum #11 @ 5" cts. B. Negative Moments = Maximum #11 @ 5" cts., except #14s @ 6" cts., may be used for long spans. 4. Live Load Deflection - AASHTO 10.6 The deflection due to service live load plus impact shall not exceed 1/800 of the span, except on bridges in urban areas used in part by pedestrains whereon the ratio preferably shall not exceed 1/1000.
##### 751.40.8.9.1.3 Slab Longitudinal Sections

HOLLOW SLABS

END SPANS

INTERMEDIATE SPANS

 (*)Increase to maintain 6" minimum on skews (see detail) (**) By Design (6" increments measured normal to the centerline of bent) (The minimum is equal to the column diameter + 2'-6") Note:All longitudinal dimensions shown are horizontal (Bridges on grades and vertical curves, included).For Sections A-A and B-B see EPG 751.40.8.9.1.4 Slab Cross Section and Section Properties.

SOLID SLABS

END SPANS

INTERMEDIATE SPANS

(*) By Design (6" increments measured normal to the centerline of Bent) (The minimum is equal to the column diameter + 2'-6")

Note:
All longitudinal dimensions shown are horizontal (Bridges on grades and vertical curves, included).

##### 751.40.8.9.1.4 Slab Cross Section and Section Properties

 HALF SECTION A-ACENTER OF SPAN HALF SECTION B-BNEAR INTERMEDIATE BENT

 AVAILABLE SLAB DEPTHSAND VOID DATA Truck Loading T (*) "D" "E" "F" 17" and less - no voids 18" 9" 15" 21" 19" (***) 10" 16" 22" 21" 12" 18" 24" 23" 14" 20" 26" 25" 15.7" 22" 28" 26" 16.7" 23" 29" 28" 18.7" 25" 31" 30" 20.85" 27" 33" Pedestrian Overpasses T (*) "D" "E" 15" and less - no voids 16" 8" 14" 17" 9" 15" 18" 10" 16" 20" 12" 18"
PART SECTION THRU VOID
DETAIL "C"

 Notes: (*) Increase the Dimension "T" by 1/2" for #14 bars placed in the top or bottom of the slab. Increase the Dimension "T" by 1" for #14 bars placed in the top and bottom of the slab. ("T" and "D" are based on 3" clearance which includes the integral wearing surface to the top of the longitudinal bar.) (**) For Roadways with slab drains, use 10" minimum. For Roadways that require additional reinforcement for resisting moment of the edge beam 20" minimum, refer to EPG 751.40.5.1 Structure with Wearing Surface Slab Drains - Details. (***) Preferred minimum (Consult the Structural Project Manager prior to the use of a thinner slab.)

Voided Slab Spans

 Void Dia.(in.) Area(sq.ft.) Area(sq.in.) Momentof Inertia(ft.4) Momentof Inertia(in.4) Weight(lb./ft.) 8.00 0.3490 50.2656 0.0096 201.0624 52.35 9.00 0.4417 63.6174 0.0155 322.0630 66.26 10.00 0.5454 78.5400 0.0236 490.8750 81.81 12.00 0.7854 113.0976 0.0490 1017.8784 117.81 14.00 1.0690 153.9384 0.0909 1885.7454 160.35 15.70 1.3443 193.5932 0.1438 2982.4242 201.66 16.70 1.5211 219.0402 0.1841 3818.0075 228.17 18.70 1.9072 274.6465 0.2894 6002.5789 286.09 20.85 2.3710 341.4310 0.4473 9276.7336 355.65
##### 751.40.8.9.1.5 Slab Reinforcement

HOLLOW SLABS

DETAIL "A"
(POSITIVE MOMENT)

DETAIL "B"
(NEGATIVE MOMENT)

 Longitudinal Reinforcement(Largest Bar) "G" #8 3-5/8" #9 3-3/4" #10 3-7/8" #11 4" #14 4-3/8"

Moment Curves

 1. Determine reinforcing steel from the sum of the dead loads and the live loads + impact (working stress design) or design in accordance with AASHTO Article 8.16 and 8.9 (load factor design). 2. Determine the cut-off points for the stress bars in sets of 2 or 3.Maximum length = 60'-0", see AASHTO Article 8.24 for extension of reinforcement. 3. Determine the drop panel width: Minimum width = Column diameter plus 2~6".Maximum width = (Parallel to the centerline of roadway) as determined by deign). In general, the width of the drop panel normal to centerline bent should be adjusted to 6" increments.

SOLID SLABS (BOTTOM)

Use AASHTO 3.24.10 Distribution Reinforcement shall be a percentage of positive moment reinforcement (% = 100/√S, with a maximum of 50%).

EDGE BEAM

 Positive Moment: The bridge curb is not to be used in determining the resisting moment of the edge beam. Dead Load: Use the same distribution as for the slab design.Use for simple spans 0.1 PS. Live Load + I: AASHTO Article 3.24.8 Use for negative moment on continuous spans 0.1 PS.Use for positive moment on continuous spans 0.08 PS. Where P = Wheel load in pounds, see EPG 751.40.8.5.1.1 Cantilever Moment. S = Span in feet

##### 751.40.8.9.1.6 Shear

The shear in the Hollow Slab should be computed for all loadings H20 and over.

Use the same distribution for the dead and live load as was used for the moment.

Unit Shear Stress

 Load Factor: Shear Stress = ${\displaystyle \,Vu={\frac {Vu}{\phi (Bd-voids~area)}}}$ Working Stress: Shear Stress = ${\displaystyle \,v={\frac {v}{(Bd-Area~of~voids)}}}$ Where "d" = effective depth, ${\displaystyle \phi }$ = 0.85 for shear

Allowable Shear Stress

 Load Factor: ${\displaystyle \,Vc=2.0{\sqrt {f'c}}}$ Where Vc = shear strength provided by concrete Working Stress: ${\displaystyle \,Vc=0.95{\sqrt {f'c}}}$ Where Vc = Allowable shear stress carried by concrete

If shear stress (load) exceeds the allowable shear use one or more of the following solutions.

1. Eliminate some voids and replace remainder.
2. Shorten alternate voids
3. Use shear reinforcing in the critical zone.

Note:
Consider a voided slab the same as a regular slab as it pertains to the minimum stirrups (AASHTO - Article 8.19).
i.e. The minimum stirrups are not required if the shear stress is less than allowable.

##### 751.40.8.9.1.7 Camber Deflection

Ultimate Deflection:

Compute the "ultimate deflection" at 0.2 points of the spans for the dead loads without the 35# future wearing surface.

Ultimate deflection (long term) = elastic deflection x 3

 Ec (Elastic Modulus) = ${\displaystyle \,4\times 10^{6}}$ psi (districts 1 and 4) ${\displaystyle \,6\times 10^{6}}$ psi (remainder of districts)

The modulus of elasticity for the use in a continuous structure analysis computer program should be determined as follows:

 ${\displaystyle \,\Delta _{ULT}}$ = ${\displaystyle \,3\times \Delta _{ELASTIC}}$ ${\displaystyle \,\Delta _{ELASTIC}}$ = ${\displaystyle \,Coeff./E_{c}}$ ${\displaystyle \,\Delta _{ULT}}$ = ${\displaystyle \,(Coeff./E_{c}\times 3=Coeff./(E_{c}/3)}$ Where: ${\displaystyle \,\Delta }$ = deflection. ${\displaystyle \,\Delta _{ULT}}$ = Ultimate deflection ${\displaystyle \,\Delta _{ELASTIC}}$ = Elastic deflection

Example No. 1

(Assume bridge is in District 8)

 ${\displaystyle \,E_{c}}$ = ${\displaystyle \,6\times 10^{6}psi}$ ${\displaystyle \,\Delta _{ULT}}$ = ${\displaystyle \,Coeff./(6/3)=Coeff./2}$

Therefore, use 2 \times 106 psi for modulus of elasticity in the structure analysis computer program to get ultimate deflection. (*)

Example No. 2

(Assume bridge is in District 1)

 ${\displaystyle \,E_{c}}$ = ${\displaystyle \,4\times 10^{6}psi}$ ${\displaystyle \,\Delta _{ULT}}$ = ${\displaystyle \,Coeff./(4/3)=Coeff./1.333}$

Therefore, use ${\displaystyle \,1.333\times 10^{6}}$ psi for modulus of elasticity in the structure analysis computer program to get ultimate deflection. (*)

(*) Gives long term deflection as output.

##### 751.40.8.9.1.8 Slab Construction Joint Details

DETAILS OF SLAB CONSTRUCTION JOINT KEY
(FOR SLAB DEPTHS 17" OR MORE)

DETAILS OF SLAB CONSTRUCTION JOINT KEY
(FOR SLAB DEPTHS 16½" OR LESS)

VOID SPACING AT LONGITUDINAL CONSTRUCTION JOINT

#### 751.40.8.9.2 End Bents

##### 751.40.8.9.2.1 Pile Cap Bents
* See Bridge Memorandum for maximum slope of spill fill.
 SECTION THRU WING SECTION A-A

ELEVATION

PLAN (SQUARE)

 (1) Wing brace details.

PLAN (SKEWED)
(*) Use the same Dimension (centerline Curb Joint) as the opposite side when the wings are the same length.
##### 751.40.8.9.2.2 Integral Column Bents

SEISMIC PERFORMANCE CATEGORY A
(PINNED COLUMN AT TOP AND BOTTOM)

PART SECTION

 SECTION A-A PINNED COLUMN SECTION B-B

Note: If the columns at an end bent have excessive moments due to shortness of the Column or length of the span, they should be detailed as "pinned" and designed for vertical reactions only.

SEISMIC PERFORMANCE CATEGORIES B, C & D
(PINNED COLUMN AT TOP, FIXED COLUMN AT BOTTOM)

For pinned column conditions at the top, see the above details.
For fixed column conditions at the bottom and column reinforcement details.

Note: For details not shown, see integral pile cap details.

##### 751.40.8.9.2.3 Reinforcement - Pile Cap Bents
SECTION THRU END BENT
(Slab depth less than 16")

SECTION THRU END BENT
(Slab depth 16" or more)

(**) Development length for top bar minimum.

##### 751.40.8.9.2.4 Reinforcement - Wing
 ELEVATION OF WING PART SECTION THRU WING (*) Clip K bars as required to maintainminimum clearance at bottom of wing.

 SECTION A-A(K-bars not shown for clarity) PART SECTION THRUEND OF WING

Note: See _____ for barrier railing details and spacing of K-bars.

##### 751.40.8.9.2.5 Design Assumptions for Integral Piles

Seismic Performance Category A

Piles may be considered as "pinned" (for superstructure) at the pile cap and designed for vertical loads only unless they fall under the following general conditions in which case they should be checked for the loadings as specified for columns.

 1. Height from centerline of slab to "pin" is less than 15'. The location of the pinned joint is arbitratily taken as about 1/3 of the length of long piles or at a point about 10' below the natural ground line. 2. Piles having a large gross moment of inertia (cast-in-place concrete) gross I of steel BP = I x n. 3. The number of piles used on a fairly long structure is small.

Seismic Performance Categories B, C & D

Piles shall be checked for combined axial and bending stresses for seismic loading conditions. For AASHTO group loads I thru VI as applicable, follow criteria noted above for seismic performance category A.

#### 751.40.8.9.3 Intermediate Bents

##### 751.40.8.9.3.1 Integral Bents

HALF SECTION

(*) 25'-0" is the max. column spacing allowed. However, the footing pressure may be the controlling factor for the column spacing. It is suggested that a rough check be made of the footing pressure before the spacing is definitely established.

In congested areas, when it is desired to keep the number of columns to a min., larger column spacings may be desirable. (consult the Structural Project Manager).

In general, use two 2'-6" columns for Roadways thru 44'-0" and additional 2'-6" columns for wider Roadways.

SEISMIC PERFORMANCE CATEGORY A

HALF SECTION

PART SECTION A-A
##### 751.40.8.9.3.2 Integral Column Bent with Drop Panel
 ATTENTION DETAILER:When detailing Int. Bents on SPS the Section thru drop panel shall be drawn to appropriate grade. PART SECTION

 PART SECTION A-A(FLAT) PART SECTION A-A(GRADE OR V.C.)D = Diameter of Column

 PART PLAN - SQUARE PART PLAN - SKEWED

SECTION THRU DROP PANEL

 LargestLongitudinalSlab Bar "a" #8 1-13/16" #9, #10 & #11 2-1/16" #14 2-9/16"
For Reference Only

 LargestLongitudinalSlab Bar "a" (*) #8 & #9 2-5/8" #10 & #11 2-7/8" #14 3-3/8"

(*) Based on 3" clearance and #6 stirrups, (includes Integral W.S.) to top longitudinal bar.

(1) Standard 90° Hook.

(2) Const. joint key D/3 x D/3 x 2", D = Diameter of Column

##### 751.40.8.9.3.3 Integral Pile Cap Bents with Drop Panel
 PART SECTION PART SECTION A-A(FLAT)

 Bottom or drop panel to be parallel to top of slab both transversely and longitudinally. (1)Horizontal except for superelevated structures. (2) Use 3" Min. clip on beam for skews above 35°. PART SECTION A-A(GRADE OR V.C.)

 PART PLAN - SQUARE PART PLAN - SKEWED

REINFORCEMENT

HALF SECTION

SECTION THRU DROP PANEL

(1) Use 5 1/4" for computing length of stirrup bar. Do not detail on plans.

(2) Standard 90° hook.

(3) Optional Const. Joint Key 10" x 2"

##### 751.40.8.9.3.4 Integral Pile Cap Bents without Drop Panel

REINFORCEMENT

HALF SECTION

SECTION THRU BENT

(1) Use 5 1/4" for computing length of stirrup bar. Do not detail on plans.

(2) Horizontal except for superelevated structures.

(3) Standard 90° hook.

##### 751.40.8.9.3.5 Pile Footing Design and Details

(1) GENERAL

Number, size and spacing of piling shall be determined by computing the pile loads and applying the proper allowable overstresses.

Group IV temperature and shrinkage moments with applicable vertical loads.

1983 AASHTO guide specifications for seismic design of highway bridges. (See chapter 4 for earthquake loads combined with applicable vertical loads.) (*) (See Structural Project Manager or Liaison)

Internal stresses including the position of the shear line shall then be computed.

Long narrow footings are not desirable and care should be taken to avoid the use of an extremely long footing 6~0" wide when a shorter footing 8'-3" or 9'-0" wide could be used.

When using the load factor design method for footings, design the number of piles needed based on the working stress design method.

ASSUMPTIONS (Bents with 2 or more columns)

SEISMIC PERFORMANCE CATEGORY A

1. Dead and live load moments will be 25% of the moments used for slab and top of Column design.
2. Temperature moments shall be 50% of the moment at top of Column.
3. Column reinforcement to be same as that required at top of Column. Footing dowel's to be #5 bars, same number as column bars.
4. Footings to be proportioned for conditions as specified. Do not use ratio of bent height as specified for Intermediate Bents for longitudinal footings dimensions.

SEISMIC PERFORMANCE CATEGORIES B, C & D

1. For Seismic Performance categories B, C & D, the connection between the bottom of Column and the footing is a fixed connection.
2. Footing design is based on (Seismic Design of Beam-Column Joint).

(*) The design of all bridges in seismic performance B, C & D are to be designed by earthquake criteria in accordance with EPG 751.9 LFD Seismic.

P = N/n ± M/S
n = number of piles
M = overturning moment
if minimum eccentricity controls the moment in both directions, it is necessary to use the moment in one direction (direction with less section modulus of Pile group) only for the footing check.
S = Section Modulus of pile group

AASHTO GROUP I AND IV LOADS

Maximum P = Pile Capacity Minimum P = 0

Tension on a pile will not be allowed for any combination of forces.

POINT BEARING PILES

(**) Maximum P = Pile capacity x 2

(I.E. for HP 10 x 42 piles, maximum P = 56 x 2 = 112 tons/pile).

Minimum P = Use allowable uplift force specified for piles in EPG 751.39 Seal Course.

(**) Two (2) is our normal factor of safety. Under earthquake loadings only the point bearing pile and rock capacities are their ultimate capacities.

FRICTION PILES

Maximum P = Pile capacity

(3) INTERNAL STRESSES

A) Shear Line
B) Bending
C) Distribution of Reinforcement
D) Shear
##### 751.40.8.9.3.6 Pedestal Pile

GENERAL

No concrete bell shall be used without approval of Structural Project Manager or Liaison.

SEISMIC PERFORMANCE CATEGORY A

1. Assume column to be "pinned" for belled footing sitting on rock. All loads will be axial.
2. Assume column to be fixed for pedestal pile embedded in rock.
3. All earth loads within the diameter of belled footing, or pedestal pile if there is no bell, above ground line shall be included in footing design.

SEISMIC PERFORMANCE CATEGORY B, C & D

See (Seismic Design).

DETAILS

SEISMIC PERFORMANCE CATEGORY A

 Diameterof Shaft MinimumBell Diameter MaximumBell Diameter Minimum(*) Reinf. Cubic YardsConcrete per ft. 2'-0" 2'-4" 6'-0" 8-#7 0.1164 2'-6" 2'-10" 7'-6" 8-#9 0.1818 3'-0" 3'-6" 9'-0" 11-#9 0.2618 3'-6" 4'-0" 10'-6" 14-#9 0.3563 4'-0" 4'-6" 12'-0" 19-#9 0.4654 4'-6" 5'-0" 13'-0" 24-#9 0.5890 5'-0" 5'-6" 14'-0" 29-#9 0.7272 5'-6" 6'-0" 15'-0" 35-#9 0.8799 6'-0" 6'-6" 16'-0" 41-#9 1.0472

Concrete Quantities shown in table are per linear foot of shaft only. Bell Quantities are not included.

(*) Amount of reinforcing may be increased from that shown to meet the individual job requirements.

Minimum reinforcement meets AASHTO Spec. 8.18 for reinforcement of compression members.

DETAILS

SEISMIC PERFORMANCE CATEGORY B, C & D

 Diameterof Shaft Minimum(*) Reinf. Cubic YardsConcrete per ft. 2'-0" 8-#7 0.1164 2'-6" 8-#9 0.1818 3'-0" 11-#9 0.2618 3'-6" 14-#9 0.3563 4'-0" 19-#9 0.4654 4'-6" 24-#9 0.5890 5'-0" 29-#9 0.7272 5'-6" 35-#9 0.8799

Concrete Quantities shown in table are per linear foot of shaft only.

(*) Amount of reinforcing may be increased from that shown to meet the individual job requirements.

Minimum reinforcement meets AASHTO Spec. 8.18 for reinforcement of compression members.

(**) Stay in place casing may be used in place of spirals for column diameters greater than 4 foot.

### 751.40.8.10 Prestressed Concrete I-Girders

#### 751.40.8.10.1 Design

##### 751.40.8.10.1.1 Girder Design

Geometric Dimensions

Girder Analysis (Continuous Span Series)

Stresses due to dead load weight of slab, girder, diaphragms, haunch and forms will be based on simple spans from centerline to centerline of bearings.

Stresses due to dead load weight of curbs, parapet, rails, future wearing surface and outlets will be based on continuous composite spans with loads equally distributed to all girders. The span lengths used in these computations will be based on the distance from the centerline of the bearing at the End Bent to the centerline of the Int. Bent, and from centerline of Int. Bent to centerline of Int. Bent.

Stresses due to live load plus impact will be based on continuous composite spans whose lengths are described above for curbs, etc.

The analysis will be made on the basis of transformed areas of all steel (both strands and bars) in the section using concrete with ${\displaystyle \,n}$ = 6.

In composite design, allowances shall be made for the difference in modulus of elasticity of slab and girder by using the effective slab area as specified for concrete T-Beams as given in the current AASHTO Specifications, multiplied by the factor ${\displaystyle \,(E_{slab}/E_{girder})}$ . The area shall include the transformed area of all longitudinal reinforcing bars within the effective width. The 1" integral wearing surface shall not be used in the effective slab depth.

Effective Flange Width

The effective flange width for Beam Types 2,3,4 & 6 should be calculated using AASHTO 8.10.1. For Beam Type 7, the effective flange width should be calculated using AASHTO 9.8.3.

Continuity at Intermediate Supports

Continuity will be obtained at intermediate supports by pouring a concrete diaphragm monolithic with the deck slab and encasing the prestressed girders. Reinforcing bars will tie the slab, diaphragms and girders together.

Reinforcing bars, ${\displaystyle \,f_{y}}$ = 60,000 psi, will be placed in the deck slab for tensile steel.

The ultimate negative moments should be 2.17 times the maximum live load moments including impact and 1.3 times moments for future wearing surface and dead load of barrier or railing.

The area of longitudinal reinforcing steel at the centerline of the intermediate bent should be determined on the basis of a cracked section. This area of reinforcing bars is to be provided by adding additional bars between the normal longitudinal bars at the top of the slab. #8 maximum bar size for additional bars over bents.

These special negative moment reinforcing bars should be ended by one of the following criteria (whichever is greater):

1. Where the stress on the normal longitudinal reinforcing bars does not exceed 24,000 psi. as based on a cracked section, plus 15 bar diameters or development length.
2. Not closer to the centerline of the intermediate bent than 1/10 of the span. (8' min.)

The concrete stress at the bottom of the girder should be checked at a point 70 strand diameters plus 9 inches from the centerline of the intermediate bent to see that the total compressive stress due to prestress and negative moment does not exceed 3,000 psi. (AASHTO. 9.7.2)

The positive moment at the intermediate bent should be provided for by extending the top two rows of the top strands (both straight or deflected) and if available, the number of bottom strands indicated in tables below bent to form a right angle hook.

Design of Negative Moment Reinforcement

Since most of the dead load moments are carried by the beam acting as a simple span, the negative design moment over piers is the live load plus impact moment. In most designs, the dead load applied after continuity is achieved should also be considered in the negative design moment. The effect of initial precompression due to prestress in the precast girders may be neglected in the negative moment computation of ultimate strength if the maximum precompression stress is less than ${\displaystyle \,0.4f'_{c}}$ and the continuity reinforcement is less than 1.5 percent.

It will usually be found that the depth of the compression block will be less than the thickness of the bottom flange of the precast girder. For this reason, the negative moment reinforcement required can be determined by assuming the beam to be a rectangular section with a width equal to the bottom flange width of the girder. Due to the lateral restraint of the diaphragm concrete, ultimate negative compression failure in the PCA tests always occurred in the girders, even though the diaphragm concrete strength was about 1000 psi less than that of the girder concrete for this reason, it is recommended that the negative moment reinforce-ment be designed using the compressive strength of the girder concrete.

Rectangular Beam Curves

Web
Thickness
(Inches)
Number of Bottom Strands for Positive Moment
Connection (C) for Closed Diaphragms
Beam Type 2
or Modified
Beam Type 3
or Modified
Beam Type 4
or Modified
Beam Type 6
or Modified
Beam Type 7
or Modified
6 6 8 10 -- 18
6 1/2 -- -- -- 14 --
7 (A) 8 10 10 -- --
7 1/2 (B) -- -- -- 16 --
8 (A) 8 10 12 -- --
8 1/2 (B) -- -- -- 16 --

Web
Thickness
(Inches)
Number of Bottom Strands for Positive Moment Connection (C) for
Open Intermediate Diaphragms with Continuous Superstruecture
Beam Type 2
or Modified
Beam Type 3
or Modified
Beam Type 4
or Modified
Beam Type 6
or Modified
Beam Type 7
or Modified
6 12 16 16 -- 22
6 1/2 -- -- -- 22 --
7 (A) 12 16 16 -- --
7 1/2 (B) -- -- -- 22 --
8 (A) 12 16 16 -- --
8 1/2 (B) -- -- -- 22 --

 (A) Modified Beam Type 2, 3 or 4. (B) Modified Beam Type 6. (C) If available, otherwise bend all bottom strands.

Negative Moment Bar Cut-Off (Working Stress Controlling)

Area of slab bars required and stress in the slab bars are printed in program BR200.

Determine stress of the area of slab bars input into program at a point where the area required is larger than that input.

Interpolate along a straight line to where the stress is 24,000 psi.

Note: Negative moment bar computations use a cracked section analysis to determine stresses.

##### 751.40.8.10.1.2 Allowable Concrete Stresses

The following criteria is shown for clarity and is in accordance with AASHTO 9.15.

${\displaystyle \,f'_{c}}$ = 5,000 psi,   ${\displaystyle \,f'_{ci}}$ = 4,000 psi

A. Temporary stresses before losses except as noted:

• Compression...${\displaystyle \,0.6f'_{ci}=0.6\times 4,000psi=2,448psi}$ (*)
• Tension
• Precompressed tensile zone ....................
• No temporary allowable stresses are specified. See paragraph "B" below.
• In tension areas with no bonded reinforcement...${\displaystyle \,3{\sqrt {f'_{ci}}}=3{\sqrt {4,000}}=190psi}$
• Where the calculated tensile stress exceeds this value, bonded reinforcement shall be provided to resist the total tension force in the concrete computed on the assumption of an uncracked section. The maximum tensile stress shall not exceed...${\displaystyle \,7.5{\sqrt {f'_{ci}}}=7.5{\sqrt {4,000}}=475psi}$

B. Stresses at service loads after losses:

• Compression...${\displaystyle \,0.4f'_{c}=0.4\times 5,000=2,000psi}$
• Tension in the precompressed tensile zone...
• (a) For members with bonded reinf. (**)...${\displaystyle \,6{\sqrt {f'_{c}}}=6{\sqrt {5,000}}=425psi}$
• (b) For members without bonded reinf...${\displaystyle \,=Zero}$
• Tension in other areas
• Tension in other area is limited by the allowable temporary stresses specified in "A" above.

C. Cracking stress:

• Modulus of rupture from tests or (for normal weight concrete)...${\displaystyle \,7.5{\sqrt {f'_{c}}}=7.5{\sqrt {5,000}}=530psi}$

• Tension in negative moment reinforcement...${\displaystyle \,f_{y}}$ = 60,000 psi,   ${\displaystyle \,f_{s}}$ = 24,000 psi
• Compression in concrete at bottom of girder...${\displaystyle \,f'_{c}}$ = 5,000 psi,   ${\displaystyle \,f_{c}=0.6f'_{c}}$

(*) BR200 allows 2% overstress

(**)Strands qualify if not debonded at ends.

##### 751.40.8.10.1.3 Prestress Loss and Prestress Camber

${\displaystyle \,{\Bigg [}{\cfrac {{\overset {(SH)}{6,000}}+{\overset {(ES)}{\frac {Es}{Ec_{i}}}}fc+{\overset {(CR_{C})}{8.5fc}}+(5,000-{\overset {(CR_{s})}{0.1ES}}-0.05(SH+CR_{c}))}{fs_{i}}}{\Bigg ]}}$

 Reduce to:     ${\displaystyle \,{\cfrac {10,700+(0.9\left({\frac {E_{s}}{Ec_{i}}}\right)+8.08)fc}{fs_{i}}}}$ ${\displaystyle \,SH}$ = Shrinkage ${\displaystyle \,ES}$ = Elastic Strain ${\displaystyle \,CR_{c}}$ = Concrete Creep ${\displaystyle \,CR_{s}}$ = Steel Creep

 ${\displaystyle \,CR_{c}}$ = ${\displaystyle \,12fc_{ir}-7fc_{ds}}$ ${\displaystyle \,CR_{c}}$ = ${\displaystyle \,12fc-7/2fc=8.5fc}$  (Approximate Estimate) ${\displaystyle \,Ec_{i}}$ = ${\displaystyle \,150^{1.5}33{\sqrt {f'c_{i}}}}$     ${\displaystyle \,ES={\frac {Es}{Ec_{i}}}fc_{ir}={\frac {Es}{Ec_{i}}}fc}$  (Approximate Estimate) ${\displaystyle \,fc_{ir}}$ = Concrete stress at centroid of P/S steel at point considered due to P/S and dead load at release. ${\displaystyle \,fc}$ = ${\displaystyle \,fc_{ir}}$ (Assume ${\displaystyle \,fc_{ir}=fc}$) ${\displaystyle \,fc}$ = ${\displaystyle \,0.4(4,000)=1,600psi}$ (Estimate average) ${\displaystyle \,fc_{ds}}$ = Concrete stress at centroid of P/S Steel (due to dead load)(Assume fcds = 1/2 fc) ${\displaystyle \,fs_{i}}$ = Initial stress in P/S steel ${\displaystyle \,fs_{i}}$ = ${\displaystyle \,270,000psi\times 75\%=202,500psi}$ ${\displaystyle \,Ec_{i}}$ = ${\displaystyle \,150^{1.5}33{\sqrt {4,000}}=3,834,253.5psi}$ ${\displaystyle \,Es}$ = ${\displaystyle \,28,000,000psi}$ (AASHTO 9.16.2.1) ${\displaystyle \,{\frac {Es}{Ec_{i}}}}$ = ${\displaystyle \,7.30}$

${\displaystyle \,{\frac {10,700+(0.9\times 7.30+8.08)1,600}{202,500}}=16.9\%}$

${\displaystyle \,202.5ksi\times 16.9\%=34.22ksi}$

Total loss due to all causes, except friction, is 34.22 ksi. (Friction losses are applied to post-tensioned girder only.) Use 8.84% for initial loss and 8.84% for final loss for design.

${\displaystyle \,202.5ksi\times 8.84\%=17.90ksi}$ = initial loss

${\displaystyle \,202.5-17.90=184.60ksi}$

${\displaystyle 184.60ksi\times 8.84\%=16.32ksi}$ = final loss

${\displaystyle 17.90+16.32=34.22ksi\approx 34.22ksi=202.5ksi\times 16.9\%}$ = total loss

In the above design example, if tension exceeds AASHTO Specifications, (425 psi for 5,000 psi concrete) the girder will have to be modified to limit stress to 425 psi.

 ${\displaystyle \,f'c}$ = 6,000 psi ${\displaystyle \,f'c_{i}}$ = 4,500 psi Grade 270 low relaxation strands ${\displaystyle \,fc}$ = ${\displaystyle \,0.4(4,500)=1,800psi}$ (Estimated average) ${\displaystyle \,Ec_{i}}$ = ${\displaystyle \,150^{1}.533{\sqrt {f'c_{i}}}=4,066.840psi}$ ${\displaystyle \,{\frac {Es}{Ec}}}$ = ${\displaystyle \,{\frac {28,000,000}{4,066,840}}=6.89}$ AASHTO 9.16.2.1.3: ${\displaystyle \,CRc=12fc-7/2fc=8.5fc}$ (approximate estimate)

${\displaystyle \,{\Bigg [}{\overset {(SH)}{6,000}}+{\overset {(ES)}{\frac {Es}{Ec_{i}}}}fc+{\overset {CR_{c})}{8.5fc}}+(5,000-{\overset {(CR_{s})}{0.1ES}}-0.05(SH+CR_{c})){\Bigg ]}}$

Reduce to:   ${\displaystyle \,{\cfrac {10,700+(0.9({\frac {Es}{Ec_{i}}})+8.08)fc}{fs_{i}}}}$

 ${\displaystyle \,fc}$ = ${\displaystyle \,0.4(4,500)=1,800psi}$ (estimated average) ${\displaystyle \,{\frac {Es}{Ec_{i}}}}$ = ${\displaystyle \,6.89}$

${\displaystyle \,fs_{i}}$ = Initial stress in low relaxation strands stressed to 75% of ultimate (*)

${\displaystyle \,fs_{i}}$ = 270,000 psi \times 75% = 202,500 psi

${\displaystyle \,{\frac {10,700+(0.9\times 6.89+8.08)\times 1,800}{202,500}}=18.0\%}$

${\displaystyle \,202.50ksi\times 18.0\%=36.45ksi}$ = total loss except friction

Use 9.44% for initial loss and 9.44% for final loss.

${\displaystyle \,202.50ksi\times 9.44\%=19.12ksi}$ = initial loss

${\displaystyle \,202.5-19.12=183.38ksi}$

${\displaystyle \,183.38ksi\times 9.44\%=17.31ksi}$ = final loss

${\displaystyle \,19.12+17.31=36.43ksi\approx 36.45ksi=202.5ksi\times 18.0\%}$ = total loss

P/s force initial = ${\displaystyle \,(183.38ksi)(0.153in.^{2}/strands)(no.\ of\ strands)}$

P/s force final = ${\displaystyle \,((202.5-36.43)ksi)(0.153in.^{2}/strand)(no.\ of\ strands)}$

(*) Suggested by FHWA: when using 3/8" round strands, max. ${\displaystyle \,fs_{i}=0.7\times 250ksi\ or\ 0.7\times ultimate\ stress}$, whichever is smaller. Larger initial stresses will cause debonding.

Prestress Concrete Girder Formula for Stress Calculation

(-) Tension;   (+) Compression

Temp. Stress

 Allow Top ${\displaystyle \,7.5{\sqrt {f'c_{i}}}=0.474ksi}$ tension for ${\displaystyle \,f'c_{i}=4,000psi}$ Bottom ${\displaystyle \,0.6f'c_{i}=2.4ksi}$ compression for ${\displaystyle \,f'c_{i}=4,000psi}$
Temp. Top =
${\displaystyle \,{\frac {(1.0-initial\ loss)(P/S\ F)}{Ag}}-{\frac {(1.0-initial\ loss)(P/S\ F)(ECC_{nc}}{St_{nc}}}+{\frac {M_{Gdr}}{St_{nc}}}}$

Temp. Bottom =
${\displaystyle \,{\frac {(1.0-initial\ loss)(P/S\ F)}{Ag}}-{\frac {(1.0-initial\ loss)(P/S\ F)(ECC_{nc}}{Sb_{nc}}}+{\frac {M_{Gdr}}{Sb_{nc}}}}$

 Allow Top ${\displaystyle \,0.4\ f'c=2.0ksi}$ compression for ${\displaystyle \,f'c=5,000psi}$ Bottom ${\displaystyle \,6.0{\sqrt {f'c}}=0.424ksi}$ tension for ${\displaystyle \,f'c=5,000psi}$
Top final =
${\displaystyle \,Temp.\ Top\ Stress-{\frac {(Final\ loss)(P/S\ F)}{A_{c}}}+{\frac {(Final\ loss)(P/S\ F)(ECC_{c})}{St_{c}}}+{\frac {M_{Slb+Dph}}{St_{nc}}}+{\frac {M_{DLC}}{St_{c}}}{st_{c}}+{\frac {M_{LL+I}}{St_{c}}}}$

Bottom final =
${\displaystyle \,Temp.\ Bott.\ Stress-{\frac {(Final\ loss)(P/S\ F)}{A_{c}}}-{\frac {(Final\ loss)(P/S\ F)(ECC_{c})}{Sb_{c}}}-{\frac {M_{Slb+Dph}}{Sb_{nc}}}-{\frac {M_{DLC}}{Sb_{c}}}-{\frac {M_{LL+I}}{Sb_{c}}}}$

0.153 sq. in. = Area of one 1/2 inch strand
270 ksi = f's = Ult, Str. P/S Strand
202.5 ksi = 0.75 (270) = Initial steel stress

0.0884 = 8.84% Initial loss - low relaxation
0.0884 = 8.84% Final loss - low relaxation
4 Str. 2 Draped
202.5 (0.153) = 30.98 kips/Str. P/s force
6 Strands (30.98) = 185.90 P/s force

 ${\displaystyle \,A_{c}}$ = Area Composite ${\displaystyle \,A_{g}}$ = Area Girder ${\displaystyle \,Ecc_{c}}$ = Eccentricity of prestress force of composite section ${\displaystyle \,Ecc_{nc}}$ = Eccentricity of prestress force of non-composite section ${\displaystyle \,M_{DFLC}}$ = Composite dead load moment ${\displaystyle \,M_{Gdr}}$ = Girder dead load moment ${\displaystyle \,M_{LL+I}}$ = Live load + impact moment ${\displaystyle \,M_{Slb+Dph}}$ = Slab + diaphragm moment ${\displaystyle \,P/S\ F}$ = Prestress forces in girder ${\displaystyle \,Sb_{c}}$ = Composite section modulus at bottom of girder ${\displaystyle \,Sb_{nc}}$ = Non-composite section modulus at bottom of girder ${\displaystyle \,St_{c}}$ = Composite section modulus at top of girder ${\displaystyle \,St_{nc}}$ = Non-composite section modulus at top of girder

Prestress Camber

Reference: Computer Program BR139B

${\displaystyle \,{\begin{Bmatrix}I4=107,888in.^{4}\\(non-transformed)\\Beam\ wt.=0.541\ (k/ft.)\end{Bmatrix}}}$   Used to resist uplift before beam is set on bent.

${\displaystyle \,{\begin{Bmatrix}I4=114,383in.^{4}\\(transformed)\\Slab\ wt.=0.92\ (k/ft.)\\Diaphragm\ wt.=2.65\ (K)\end{Bmatrix}}}$   Used after beam is in place.

Mult. factor   ${\displaystyle \,[1+(1-e^{-\phi })]=1.77}$
 Mult. Factor ${\displaystyle \,(F)}$ ${\displaystyle \,f'c}$ = 5,000psi ${\displaystyle \,f'c}$ = 6,000psi Beam Type 3 1.780 1.773 Beam Type 4 1.772 1.765 Beam Type 4 1.775 1.768 Beam Type 6 1.761 1.754
${\displaystyle \,F}$ = 1.77
${\displaystyle \,e}$ =2.718
${\displaystyle \,\phi }$ = \varepsilon\ creep \times E_{28\ days}
${\displaystyle \,\varepsilon \ creep}$ = (See page 3 PCA design of precast prestressed concrete girders. Use 40% factor based on creep at erection for 28 days.)

The following formulas are used to determine:

• Camber due initial strand stress (inch),
• deflection due beam weight (inch),
• camber due strands, beam weight and 28 day creep (inch),
• camber L/4 due strands, beam weight and 28 day creep (inch),
• deflection due to slab weight (inch),
• camber centerline due strands, beam weight, 28 day creep, slab and diaphragm (inch), and
• camber quarterpoint due strands, beam weight, 28 day creep, slab and diaphragm (inch).

Formulas used:

Positive deflect up ${\displaystyle \,\uparrow }$

Negative deflect down ${\displaystyle \,\downarrow }$

${\displaystyle \,\uparrow \triangle _{1}=144\times 10^{3}\times {\underset {(a={\big [}L-(centerline\ to\ centerline\ tie\ downs){\big ]}\div 2)ft.}{{\Bigg [}{\frac {F_{01}(e_{1})(L_{2}}{8E_{i}I}}+{\frac {F_{02}(e_{2}+e_{3}}{E_{i}I}}{\Bigg (}{\frac {L_{2}}{8}}-{\frac {a^{2}}{6}}{\Bigg )}-{\frac {F_{02}(e_{3}(L^{2})}{8E_{i}I}}{\Bigg ]}}}}$

Beam weight camber

${\displaystyle \,\downarrow \triangle _{2}={\frac {5W_{B}(L^{4})}{384E_{i}I}}(1728\times 10^{3})}$

Slab weight camber

${\displaystyle \,\downarrow \triangle _{s}={\Bigg [}{\frac {5W_{s}(L^{4})}{384E_{f}I_{TR}}}+{\frac {P(L^{3})}{48E_{f}I_{TR}}}+{\frac {2PsX(3L^{2}-4X^{2})}{48E_{f}I_{TR}}}{\Bigg ]}(1728\times 10^{3})}$

Force straight strands (1/2" low relaxation strands)

${\displaystyle \,F_{01}=(no.\ of\ straight\ strands)\times {\big [}31.0-(17.1\times 0.153){\big ]}kips}$

Force draped strands ( 1/2 " low relaxation strands)

${\displaystyle \,F_{02}=(no.\ of\ draped\ strands)\times {\big [}31.0-(17.1\times 0.153){\big ]}kips}$

${\displaystyle \,270ksi\times 75\%\times (0.153sq.\ in.)=31\ kips\ per\ strand}$
${\displaystyle 202.5\times (1-0.0884)=184.6ksi}$
${\displaystyle 184.6\times (1-0.0884)=168.28ksi}$
${\displaystyle 202.5-168.28=34.22ksi=Total\ loss}$
${\displaystyle Average\ loss=Totalloss/2=34.22/2=17.1ksi}$

 ${\displaystyle e_{1}}$ = dist. centroid beam to centroid straight strand (in.) ${\displaystyle e_{2}}$ = dist. centroid beam to low centroid draped at center of beam (in.) ${\displaystyle e_{3}}$ = dist. centroid beam to up centroid draped at end of beam (in.) ${\displaystyle L}$ = length (ft.) (cneterline bearing to centerline bearing). ${\displaystyle I}$ = moment of inertia (in.2) non-transformed. ${\displaystyle I_{TR}}$ = moment of inertia (in.2) transformed. ${\displaystyle Ps}$ = concentrated loads due to variable slab thickness on each end. ${\displaystyle X}$ = dist. from centerline brg. to Ps. ${\displaystyle P}$ = concentrated load due to diaphragm at center of span (kips) ${\displaystyle W_{B}}$ = uniform beam load (kips/ft.) ${\displaystyle W_{S}}$ = uniform slab load (kips/ft.) ${\displaystyle F}$ = factor for 28 day creep ${\displaystyle E_{i}}$ = modulus of elasticity corresponding to initial girder concrete strength ${\displaystyle E_{f}}$ = modulus of elasticity corresponding to final girder concrete strength

${\displaystyle \,\triangle Centerline=F(\triangle _{1}-\triangle _{2})-\triangle _{s}}$

${\displaystyle \,\triangle \ at\ 0.10=0.314(\triangle \ at\ Centerline)}$
${\displaystyle \,\triangle \ at\ 0.20=0.593(\triangle \ at\ Centerline)}$
${\displaystyle \,\triangle \ at\ 0.25=0.7125(\triangle \ at\ Centerline)}$
${\displaystyle \,\triangle \ at\ 0.30=0.813(\triangle \ at\ Centerline)}$
${\displaystyle \,\triangle \ at\ 0.40=0.952(\triangle \ at\ Centerline)}$

Note: Compute and show on plans camber at 1/4 points for bridges with spans less than 75', 1/10 points for spans 75' and over.

##### 751.40.8.10.1.4 Superstructure Design

The live load distribution to girders may be assumed to be the same as the AASHTO distribution for concrete floors on steel I-Beam stringers. These factors may be found in EPG 751.40.8.2 Distribution of Loads.

The ultimate load capacity shall be not less than 1.3 times (the weight of the girder plus the weight of the slab and diaphragms plus the weight of the future wearing surface) plus 2.17 times the design live load plus impact.

Ultimate Strength

The ultimate moment on a prestressed girder as determined in accordance with the ultimate load capacity indicated above, shall not be greater than the ultimate strength determined as follows:

 Where   ${\displaystyle \,t\leq 0.2d}$ Where   ${\displaystyle \,t>0.2d}$ ${\displaystyle \,M_{u}=A_{s}f'_{s}(d-t/2)}$or${\displaystyle \,M_{u}=0.85f'_{c}bt(d-t/2)}$ Use the lesserin each case ${\displaystyle \,M_{u}=A_{s}f'_{s}(0.9d)}$or${\displaystyle \,M_{u}=0.85f'_{c}b(0.2d)(0.9d)}$

Where:

 ${\displaystyle \,A_{s}}$ = Area of p/s strands in bottom flange ${\displaystyle \,b}$, ${\displaystyle \,b'}$, ${\displaystyle \,t}$ & ${\displaystyle \,d}$ = as shown above ${\displaystyle \,f'_{s}}$ = Ultimate strength of p/s strands ${\displaystyle \,f'_{c}}$ = Ultimate strength of slab concrete = 4,000 psi

Maximum Prestressing Steel Area

${\displaystyle \,A_{s}={\frac {0.85f'_{c}bt}{f'_{s}}}}$   When   ${\displaystyle \,t\leq 0.2d}$

${\displaystyle \,a_{s}={\frac {0.85f._{c}b(0.2d)}{f'_{s}}}}$   When   ${\displaystyle \,t>0.2d}$

In lieu of the above, AASHTO - Article 9.17 & 9.18 may be used. (This is the method used by computer program BR200)

##### 751.40.8.10.1.5 Web Reinforcement

(5" Min. - 21" Max. bar spacing for #4 bars) (5" Min. - 24" Max. bar spacing for #5 bars)

(*) Prestressed concrete members shall be reinforced for diagonal tension stresses. Shear reinforcement shall be placed perpendicular to the axis of the member. The formula to be used to compute areas of web reinforcement is as follows:

${\displaystyle \,A_{V}={\frac {(V_{U}-V_{C})S}{2f_{sy}jd}}}$   Where   ${\displaystyle \,V_{C}=(0.06f'c)b'jd}$   but not more than ${\displaystyle \,180b'jd}$
But shall not be less than   ${\displaystyle \,A_{V}={\frac {100b's}{60,000}}=0.00167b's}$.

(**) Since large moments and large shears occur in the same area of the girder near the interior supports, the AASHTO formula (AASHTO - 9.20 -Shear) for computing the area of web reinforcement has been modified. The formula to be used to compute areas of web reinforcement near interior supports is as follows:

${\displaystyle \,A_{V}={\frac {(V_{U}-V_{C})S}{f_{sy}jd}};V_{C}=180b'jd}$

The value "jd" is the distance from the slab reinforcement to the center-of-gravity of the compression area under ultimate loads.

Use #4 shear reinforcement when possible. Alternate B1 bar will not work with #5.

Anchorage Zone Reinforcement - AASHTO Article 9.21.3

The following detail meets the criteria for anchorage zone reinforcement for pretensioned girders (AASHTO Article 9.21.3) for all MoDOT standard girder shapes.

 * 2 3/4" (Type 2, 3 & 4)5 1/4" (Type 6) ** 15 1/2" (Type 2, 3 & 4)22 1/2" (Type 6)

Sole Plate Anchor Studs

The standard 1/2" sole plate will be anchored with four 1/2" x 4" studs.

Studs shall be designed to meet the criteria of AASHTO Div. I-A in Seismic Performance Category C or D.

Stud capacity is determined as follows:

${\displaystyle \,Stud\ Cap.=(n)(As)(0.4Fy)(1.5)}$

Where:

 ${\displaystyle \,n}$ = no. of studs ${\displaystyle \,As}$ = area of stud ${\displaystyle \,Fy}$ = yield strength of stud (50 ksi) ${\displaystyle \,0.4Fy}$ = Allowable Shear in Pins AASHTO Table 10.32.1A ${\displaystyle \,1.5}$ = seismic overload factor

If required, increase the number of 1/2" studs to six and space between open B2 bars. If this is still not adequate, 5/8" studs may be used. The following table may be used as a guide to upper limits of dead load reactions:

The minimum 3/16" fillet weld between the
1/2" bearing plate and 1 1/2" sole plate is
 No. ofStuds StudDia. Max. Allowable D.L. Reaction (Kips) A = 0.30 A = 0.36 4 1/2" 78 65 6 1/2" 117 98 4 5/8" 122 102 6 5/8" 184 153
##### 751.40.8.10.1.6 Strands – Miscellaneous

Detensioning

In all detensioning operations the prestressing forces must be kept symmetrical about the vertical axis of the member and must be applied in such a manner as to prevent any sudden or shock loading.

General Information

Splicing:

One approved splice per pretensioning strand will be permitted provided the splices are so positioned that none occur within a member. Strands which are being spliced shall have the same "Twist" or "Lay". Allowance shall be made for slippage of the splice in computing strand elongation.

Wire failure:

Failure of one wire in a seven wire pretensioning strand may be accepted, provided that, it is not more than two percent of the total area of the strands.

Sand Blasting:

On structures where it is questionable as to the clarity of areas to be sandblasted: show limits of sandblasted area in a plan view of details on girder ends (bent sheet). However, generally, sandblasting is covered by Missouri Standard Specification 705.4.14.

#### 751.40.8.10.2 Length

##### 751.40.8.10.2.1 Structure Length
(*) Maximum length for End Bent to End Bent = 600 feet.
Typical Continuous Prestressed Structure
(Integral End Bents)

(**) Maximum length for End Bent to End Bent = 800 feet.
Typical Continuous Prestressed Structure
(Non-Integral End Bents)

#### 751.40.8.10.3 Miscellaneous Details

##### 751.40.8.10.3.1 Shear Blocks

A minimum of two Shear Blocks 12" wide x high by width of diaphragm, will be detailed at effective locations on open diaphragm bent caps when adequate structural restraint cannot be provided for with anchor bolts.

 Height of shear block shall extend a minimum of 1" above the top of the sole plate.
##### 751.40.8.10.3.2 Anchor Bolts

Simple Spans

 Note: It is permissible for the reinforcing bars and or the strands to come in contact with the materials used in forming A.B. holes. If A.B. holes are formed with galvanized sheet metal, the forms may be left in place. Hole (1 1/2" round) to be grouted with expansive type mortar.
##### 751.40.8.10.3.3 Dowel Bars
 (*) Details shown are for SPC A and B only.

Dowel bars shall be used for all fixed intermediate bents under prestressed superstructures.

Seismic Performance Category A:

Use #6 Bars @ 18" Cts. for dowel bars.

Seismic Performance Category B:

Dowel bars shall be determined by design. (#6 Bars @ 18" Cts. minimum)
Design dowel bars for shear using service load design.
Allowable stresses are permitted to increase by 33.3% for earthquake loads.

Seismic Performance Categories C & D:

See Structural Project Manager.
##### 751.40.8.10.3.4 Expansion Device Support Slots
 (*) Show these dimensions on the P/S concrete girder sheet.

### 751.40.8.11 Open Concrete Intermediate Bents and Piers

#### 751.40.8.11.1 Design

##### 751.40.8.11.1.1 General and Unit Stresses

GENERAL

Use Load Factor design method, except for footing pressure and pile capacity where the Service Load design method shall be used.

In some cases, Service Load design method may be permitted on widening projects, see Structural Project Manager.

The terms, Intermediate Bents and Piers, are to be considered interchangeable for EPG 751.40.8.11 Open Concrete Intermediate Bents and Piers.

DESIGN UNIT STRESSES

(1) Reinforced Concrete

 Class B Concrete (Substructure) ${\displaystyle \,f_{c}}$ = 1,200 psi ${\displaystyle \,f'_{c}}$ = 3,000 psi Reinforcing Steel (Grade 60) ${\displaystyle \,f_{s}}$ = 24,000 psi